u 


I 


'_  (  SYSTEM 

tfF 

GEOMETRY  AND  TRIGONOMETRY: 

TOGETHER  WITH  A 

TREATISE  OJV  SURVEYING; 

TEACHING  VARIOUS  WAYS  OF  TAKING  THE  SURVEY  OF  A  FIELD  > 
ALSO  TO  PROTRACT  THE  SAME  AND  FIND  THE  AREA. 

LIKEWISE, 

RECTANGULAR  SURVEYING; 

OR, 

AN  ACCURATE  METHOD  OF  CALCULATING  THE  AREA  OF 

ANY  FIELD  ARITHMETICALLY,  WITHOUT  THE 

NECESSITY  OF  PLOTTING  IT. 

TO  THE  WHOLE  ARE  ADDED, 

SEVERAL  MATHEMATICAL  TABLES, 

NECESSARY  FOR  SOLVING  QUESTIONS  IN 

TRIGONOMETRY  AND  SURVEYING; 

WITH  A  PARTICULAR  EXPLANATION  •  »F  THOSE  TABLES, 
AND  THE  MANNER  OF  USING  THEM. 

COMPILED  FROM  VARIOUS  AUTHORS, 

BY  ABEL  FLINT,  A.M. 


VIFTH    EDITION,    WITH    IMPORTANT    ADDITIONS, 

BY  GEORGE  GILLET, 

"SURVEYOR  GENERAL  OF  THE  STATE  Of  CONNECTICUT. 


HARTFORD  :  <    ^  •'.  • 
.PUBLISHED  BY  OLIVER  D.  COOKE  & 

1825, 


District  o/  Connecticut,  *«. 

BE  IT  REMEMBERED,  That  ou  the  twenty-fifth  day  of  September, 
in  the  forty-third  year  of  the  Independence  of  the  United  States  of 
America,  Oliver  D.  Cooke  &  Co.,  of  the  said  district,  have  deposited  in  this 
office  the  title  of  a  hook,  the  right  whereof  they  claim  as  Proprietors,  in  the 
words  folio-wing,  to  wit — 

"  A  System  of  Geometry  and  Trigonometry :  together  with  a  Treatise  on 
Surveying ;  Teaching  various  ways  of  taking  the  Surrey  of  a  Field  ;  Also  to 
Protract  the  same  and  find  the  Area.  Likewise,  Rectangular  Surveying ; 
or,  an  Accurate  Method  of  calculating  the  Area  of  any  Field  Arithmetically 
without  the  necessity  of  Plotting  it.  To  the  whole  are  added  several 
Mathematical  Tables,  necessary  for  solving  Questions  in  Trigonometry  and 
Surveying  ;  with  a  particular  explanation  of  those  Tables,  and  the  Manner 
-of  using  them.  Compiled  from  various  Authors.  By  Abel  Flint,  A.  M. 
Fifth  Edition,  with  important  Additions,  By  George  Gillet,  Surveyor  General 
of  the  State  of  Connecticut." 

"  In  conformity  to  the  Act  of  the  Congress  of  the  United  States,  entitled 
"  An  Act  for  the  encouragement  of  Learning,  by  securing  the  copies  of 
Maps,  Charts,  and  Books,  to  the  authors  and  proprietors  of  such  copies, 
during  the  times  therein  mentioned." 

R.  I.  INGERSOLL, 
Clerk  of  the  District  of  Connecticut. 
A  true  copy  of  Record,  examined  and  sealed  by  me, 

R.  I.  INGERSOLL, 
Clerk  of  the  District  of  Connecticut. 


•••*»•«••••      •     •     *   *, 


RECOMMENDATIONS 


HAVING  perused,  with  some  attention,  the  following' 
Treatise  on  Surveying,  in  Manuscript,  it  appears  to  me 
to  be  estimable  for  its  simplicity  and  perspicuity  ;  and, 
by  excluding  all  matter  but  remotely  connected  with 
the  main  subject,  and  reducing  the  Tables  of  Log- 
arithms, of  Logarithmic  Sines,  Tangents,  and  Secants, 
and  of  Difference  of  Latitude  and  Departure,  without 
impairing  their  use,  in  their  application  to  most  cases 
which  occur  in  common  Surveying,  and  supplying  any 
possible  defect  by  a  Table  of  Natural  Sines,  to  com- 
prise,  in  the  limits  of  a  pocket  volume,  whatever  is 
most  essential  and  most  useful  in  the  Art,  including  the 
important  modern  improvement  of  RECTANGULAR  SUR- 
VEYING ;  and  on  the  whole,  particularly  from  the  size 
of  the  volume,  to  be  well  adapted  to  general  use. 

JOHN  TREADWELL, 

FARMINGTON,  Sept  20tb,  1804. 


RECOMMENDATIONS. 

WE  the  subscribers  have  carefully  perused  a  Trea- 
tise on  Surveying,  prepared  for  the  Press*  by  the  Rev. 
Abel  Flint  of  Hartford  ;  and  find  it  worthy  of  the  pub- 
lic patronage.  Every  thing  not  immediately  necessarj 
for  the  practical  Surveyor  has  been  excluded  ;  while  it 
comprises  all  which  is  requisite  in  Field  Surveying,  both 
on  the  old  and  new  plan ;  elucidated  and  explained  with 
a  degree  of  conciseness  and  perspicuity  not  usually  to 
be  found  in  Treatises  on  the  same  subject.  The  Ma- 
thematical Tables  are  reduced  to  less  than  half  the  size 
occupied  by  others ;  and  any  inconvenience  which 
might  result  from  such  reduction,  is^  obviated  by  the  in- 
sertion of  a  Table  of  Natural  Sines,  not  usually  found 
in  works  of  this  nature.  The  Surveyor  who  shall  own 
this  will  not  be  under  the  necessity  of  purchasing  GIB- 
SON, which  is  a  more  expensive  work. 

ASHER  MILLER,  Surveyor  General. 
GEORGE  GILLET,  Deputy   Surveyor 
for  Tolland  County, 

MlDtLETOWN,  Oct.  3,  1804. 


PREFACE 


THE  following  work  is  chiefly  a  compilation  from 
other  Books ;  and  but  very  little  new  is  added,  ex- 
cept a  more  full  explanation,  than  has  yet  been 
published,  of  RECTANGULAR  SURVEYING,  or  the 
method  of  calculating  the  Area  of  Fields  arithme- 
tically, without  drawing  a  plot  of  them  and  mea- 
suring with  a  Scale  and  Dividers,  as  has  been  the 
common  practice  •>  and  also  a  more  particular  ex- 
planation of  the  use  of  Natural  Sines  than  is  con- 
tained in  most  Mathematical  Books. 

The  Compiler  has  endeavoured  to  render  this 
work  so  easy  and  intelligible  that  a  Learner  Will 
require  but  little  assistance  from  an  Instructer,  ex- 
cept with  regard  to  the  construction  and  use  of 
Mathematical  and  Survey  ing  Instruments.  Before, 
however,  he  eaters,  on  the  study  of  this  Book  he 
must  be  well  acquainted  with  common  Arithmetic, 
with  PecimaL  Fractions,  and  the  Square  Root; 
and  he  must  also  know  the  various  characters  or 
marks  used  in,  Arithmetic, 

A  Surveyor  will  doubtless  find  many  questions 
arise  in  the  course  of  his  practice,  for  the  solution 
of  which,  no  particular  directions  are  here  given ; 
nor  is  it  possible  to  give  directions  for  every  case 
that  may  occur.  In  all  practical  Sciences  much 
must  be  left  to  the  judgment  of  the  practitioner, 
who,  if  he  is  well  acquainted  with  the  general 
principles  of  his  Art,  will  readily  leara  to  apply 
those  principles  to  particular  cases. 

The  primary  design  of  this  treatise  is  to  teach 
common  Field  Surveying ;  at  the  same  time  it  con- 
tains the  elements  of  Surveying  upon  a  larger 


PREFACE. 

scale  ;'and  the  system  of  Geometry  and  Trigono- 
metry with  which  it  is  introduced,  with  the  Prob- 
lems for  the  mensuration  of  Superficies,  as  also  the 
Mathematical  Tables  at  the  end,  will  be  found  use- 
ful for  many  other  purposes.  It  would  be  well, 
therefore,  for  those  who  do  not  intend  to  become 
practical  Surveyors  to  acquaint  themselves  with 
what  is  here  taught ;  and  with  this  view  the  follow- 
ing work  is  very  proper  to  be  introduced  into  Aca- 
demies, and  those  higher  Schools  which  are  design- 
ed to  fit  young  men  for  active  business  in  life.  In- 
deed every  person  who  frequently  buys  and  sells 
land  should  learn  to  calculate  the  Contents  of  a 
field  arithmetically ;  a  knowledge  which  may  be 
acquired  in  a  very  little  time,  from  the  particular 
explanation  here  given  of  that  method. 

Notwithstanding;  the  many  Books  already  pub- 
lished on  the  subjects  here  treated  upon,  it  was 
thought  a  work  of  this  kind  was  really  wanted,  and 
that  if  judiciously  executed  it  would  be  useful.  It 
is  more  particularly  necessary  at  the  present  time 
in  Connecticut,  as  the  Legislature  of  the  State 
have  lately  enacted  a  Law  on  the  subject  of  Sur- 
veying, in  consequence  of  which  more  attention 
must  be  paid  to  the  Theory  of  that  Art  than  has 
been  common. 

These  considerations  induced  the  Compiler  to 
select  from  various  publications  what  appeared  to 
him  important;  and  to  arrange  the  whole  in  a 
method  best  adapted,  in  his  view,  for  teaching  that 
useful  Art.  How  far  he  has  succeeded  in  his  en- 
deavours to  simplify  the  subject,  and  render  it  easy 
to  the  Learner,  must  be  submitted  to  the  test  of 
experience. 

HARTFORD,  Conn.  October,  1804. 


PREFACE. 
A  GENERAL  VIEW  OF  THE  CONTENTS  OF  THIS  WORE. 

THE  System  of  Geometry  is  divided  into  two 
parts.  The  first  contains  Geometrical  Definitions 
respecting  Lines,  Angles,  Superficies,  &c.  The 
second  part  contains  a  number  of  Geometrical 
Problems  necessary  for  Trigonometry  and  Survey- 
ing. 

The  System  of  Trigonometry  is  also  divided 
into  two  parts :  and  teaches  the  solution  of  ques- 
tions in  Right  and  Oblique  angled  Trigonometry, 
by  Logarithms  and  also  by  Natural  Sines. 

The  Treatise  on  Surveying  is  divided  into  three 
parts.  Part  first  treats  of  measuring  Land,  and  is 
divided  into  three  Sections.  The  first  contains 
several  Problems  respecting  Mensuration,  and  for 
finding  the  Area  of  various  Right-lined  Figures 
and  Circles. 

The  second  Section  teaches  different  methods 
of  taking  the  Survey  of  Fields  ;  also  to  protract 
them,  and  find  their  Area  in  the  manner  commonly 
practised,  and  likewise  by  Arithmetical  and  Tri- 
gonometrical calculations,  without  measuring  Di- 
agonals and  Perpendiculars  with  a  Scale  and  Di- 
viders ;  interspersed  with  sundry  useful  rules  and 
directions. 

The  third  Section  is  a  particular  explanation 
and  demonstration  of  Rectangular  Surveying,  or 
the  method  of  computing  the  Area  of  Fields  from 
the  Field  Notes,  by  Mathematical  Tables,  without 
the  necessity  of  plotting  the  Field.  To  this  Sec- 
tion is  added  a  useful  Problem  for  ascertaining  the 
true  Area  of  a  Field  which  has  been  measured  by 
a  Chain  too  long  or  too  short. 


PREFACE. 

Part  second  treats  of  laying  out  Land  in  various 
shapes. 

Part  third  contains  sundry  Problems  and  Rules 
for  dividing  Land  and  determining  the  true  Course 
and  Distance  of  dividing  Lines,  or  from  one  part 
of  a  Field  to  another.  To  this  is  added  an  Appen- 
dix concerning  the  Variation  of  the  Compass  and 
Attraction  of  the  Needle  ;  also,  a  rule  to  find  the 
difference  between  the  present  Variation,  and  that 
at  a  time  when  a  Tract  was  formerly  surveyed,  in 
order  to  trace  or  run  out  the  original  lines. 

The  Mathematical  Tables,  are  a  Traverse  Ta- 
ble, or  Table  of  Difference  of  Latitude  and  De- 
parture, calculated  for  every  Degree  and  quarter 
of  a  Degree,  and  for  any  distance  up  to  50  ;  a  Ta- 
ble of  Natural  Sines  calculated  for  every  Minute ; 
a  Table  of  Logarithms  comprised  in  four  pages, 
yet  sufficiently  extensive  for  common  use  ;  and  a 
Table  of  Logarithmic  or  Artificial  Sines,  Tangents, 
and  Secants,  calculated  for  every  5  Minutes  of  a 
Degree.  To  these  Tables  are  prefixed  particular 
explanations  of  the  manner  of  using  them. 


GEOMETRY 


GEOMETRY  is  a  Science  which  treats  of  the  properties  of 
Magnitude. 

PART  I. 

Geometrical  Definitions.       + 

1.  A  Point  is  a  small  Dot;  or,  Mathematically  considered,  is 
fhat  which  has  no  parts,  being  of  itself  indivisible. 

2.  A  Line  has  length  but  no  breadth. 

3.  A  Superficies  or  Surface,  called  also  Area,  has  length  and 
breadth,  but  no  thickness. 

4.  A  Solid  has  length,  breadth,  and  thickness. 

5.  A  Right  Line  is  the  shortest  that  can  be  drawn  between 
two  Points. 

Fig.  I.        , 


G.  The  inclination  of  two  Lines  meeting 
oue  another,  or  the  opening  between  them, 
is  called  an  Angle.  Thus  at  B.  Fig.  1.  is  an 
Angle,  formed  by  the  meeting  of  the  Lines 
AB  and  BC. 


7.  If  a  right  Line  CD.  Fig.  2.  fall  upon  an- 
other Right  Line  AB,  so  as  to  incline  to  nei- 
ther side,  but  make  the  Angles  on  each  side 
equal,  then  those  Angles  are  called  Right 
Angles  ;  and  the  Line  CD  is  said  to  be  Per- 
pendicular to  the  other  Line. 


B 


GEOMETRY, 


Fig.  3, 


8.  An  Obtuse  Angle  is  greater  than  a  Right 
Angle;  as  ADE.  Fig.  3. 

9.  An   Acute  Angle   is  less  than  a  Right 
Angle;  as  EDB.  Fig.  3. 


Note.  When  three  letters  are  used  to  express  aa  Angle,  thr 
middle  letter  denotes  the  angular  Point. 


Fig.  4. 


10.  A  Circle  is  a  round  Figure,  bounded 
by  a  Line  equally  distant  from  some  Point, 
which  is  called  the  Centre.  Fig.  4. 

11.  The  Circumference  or   Periphery  of 
a  Circle  is  the  bounding  Line  ;    as  ADEB. 
Fig.  4. 

12.  The    Radius  of   a   Circle  is   a  Line 
drawn  from  the  Centre  to  the  Circumference  ; 
as  CB.  Fig.  4.     Therefore  all  Radii  of  the 
same  Circle  are  equaK 

13.  The  Diameter  of  a  Circle  is  a  Right 
Line  drawn  from  one  side  of  the  Circumfer- 
ence to  the  other,  passing  through  the  Centre ; 
and  it  divides  the  Circle  into  two  equal  parts, 
called  Semicircles ;  as  AB  or  DE.  Fig.  5. 

14.  The  Circumference  of  every  Circle  is 
supposed  to  be  divided  into  360  equal  part?, 
called    Degrees ;  and  each   Degree   into   60 
equal  parts,  called  Minutes  ;  and  each  Minute 

into  60  equal  parts,  called  Seconds  ;  and  these  into  Thirds,  &c. 

JVote.  Since  all  Circles  are  divided  into  the  same  number  ot 
Degrees,  a  Degree  is  not  to  be  accounted  a  quantity  of  any 
determinate  length,  as  so  many  inches  or  feet,  &c.  but  is 
always  to  be  reckoned  as  being  the  360th  part  of  the  Cir~ 
cumference  of  any  Circle,  without  regarding  the  bigness- 
of  the  Circle. 

15.  An  Arch  or  Arc  of  a  Circle  is  any  part  of  the  Circumfer- 
euce  ;  as  BF  or  FD.  Fig.  5  ;  and  is  said   to  be  an  Arch  of  so 
many  Degrees  as  it  contains  pacts  of  360  into  which  the  whok 
Circle  is  divided. 


GEOMETRY 


11 


16.  A  Chord  is  a  Right  Line  drawn  from 
one  end  of  an  Arch  to  the  other,  and  is  the 
measure  of  the  Arch  ;  as  HG  is  the  Chord  of 
the  Arch  HIG.  Fig.  6. 


Fig.  7. 


.  The  Chord  of  an  Arch  of  60  degrees  is  equal  in  length 
to  the  Radius  of  the  Circle  of  which  the  Arch  is  a  part. 

17.  The  Segment  of  a  Circle  is  a  part  of  a  Circle,  cut  off  by 
a  Chord  ;  thus  the^pace  comprehended  between  the  Arch  HIG 
and  the  Chord  HG  is  called  a  Segment.     Fig.  6. 

18.  A  Quadrant  is  one  quarter  of  a  Circle  ;  as  ACB.     Fig.  6. 

19.  A  Sector  of  a  Circle   is  a  space  contained  between  two 
Radii  and  an  Arch  less  than  a  Semicircle ;  asBCDorACD, 
Fig.  6. 

20.  The  Sine  of  an  Arch  is  a  Line  drawn 
from  one  end  of  the  Arch,  perpendicular  to 
the  Radius  or  Diameter  drawn  through  the 
other  end  :  Or,  it  is  half  the  Chord  of  double 
the  Arch ;  thus  HL  is  the  Sine  of  the  Arch 
HB.  Fig.  7. 

21.  The  Sines  on  the  same  Diameter  in- A 
crease  in  length  till  they  come  to  the  Centre, 
and  so  become  the  Radius.     Hence  it  is  plain 
that  the  Radius  CD  Fig.  7.  is  the  greatest 
possible  Sine,  or  Sine  of  90  Degrees. 

22.  The  Versed  Sine  of  an  Arch  is  that  part  of  the  Diameter 
or  Radius  which  is  between  the  Sine  and  the  Circumference  ? 
thus  LB  is  the  Versed  Sine  of  the  Arch  HB.  Fig.  7. 

23.  The  Tangent  of  an  Arch  is  a  Right  Line  touching  the 
Circumference,  and  drawn  perpendicular  to  the  Diameter  ;  ami 
is  terminated  by  a  Line  drawn  from  the  Centre  through  the 
other  end  of  the  Arch  ;  thus  BK  is  the   Tangent  of  the  Arch 
BH.  Fig.  7. 

JVote.  The  Tangent  of  an  Arch  of  45  Degrees  is  equal  in 
length  to  the  Radius  of  the  Circle  of  which  the  Arch  i^a 
part. 


.  The  Secant  of  an  Arch  is  a  Line  drawn  from  the  Centre 


12  GEOMETRY. 

through  one  end  of  the  Arch  till  it  meets  the  Tangent  ;  thus- 
CK  is  the  Secant  of  the  Arch  BH.  Fig.  7. 

25.  The  Complement  of  an  Arch  is  what  the  Arch  wants  of 
90  Degrees,  or  a  Quadrant  ;  thus  HD  is  the  Complement  of  the 
Arch  BH.  Fig.  7.  ^ 

26.  The  Supplement  of   an  Arch  is   what  the   Arch  wants 
of  180  Degrees,  or  a  Semicircle  ;  thus  ADHis  the  Supplement 
of  the  Arch  BH.  Fig.  7. 

27.  The  Sine,  Tangent  or  Sejant  of  the  Complement  of  any 
Arch  is  called  the  Co-Sine,  Co-Tangent,  or  Co-Secant  of  the 
Arch  ;  thus,  FH  is  the  Sine,  Dl  the  Tangent,  and  Ci  the  Secant 
of  the  Arch  DH  ;  or  they  are  the  Co-Sine,  Co-Tangent,  and  Co- 
Secant  of  the  Arch  BH.  Fig-.  7. 

28.  The  measure  of  an  Angle  is  the  Arch  of  a  Circle  con- 
tained  between  the  two  Lines  which  form  me  angle,  the  angular 
Point  being  the  Centre  ;  thus,  the  Angle  HCB.  Fig.  7.  is  mea- 
sured by  the  Arch  BH  :  and  is  said  to  contain  so  many  Degrees 
m  the  Arch  does. 

• 

Note.  An  Angle  is  esteemed  greater  or  less  according  to  the 
opening  of  the  Lines  which  form  it,  or  as  the  Arch  inter^ 
cepted  by  those  Lines  contains  more  or  fewer  Degrees. 
Hence  it  may  be  observed,  that  the  bigness  of  an  Angle 
does  not  depend  at  all  upon  the  length  of  the  including 
Lines  ;  for  all  Arches  described  on  the  same  Point,  and 
intercepted  by  the  same  Right  Lines,  contain  exactly  the 
same  number  of  Degrees,  whether  the  Radius  be  longer  or 
shorter. 

29.  The  Sine,  Tangent,  or  Secant  of  an  Arch  is  also  the  Sine; 
Tangent,  or  Secant  of  the  Angle  whose  measure  the.  Arch  is. 

Fi.  8. 


30.  Parallel  Lines  are  such  as  are  equally  -&,  -  B 
distant  from  each  other  ;    as  AB   and  CD. 

Fig.     8r 


31.  A  Triangle  is  a  Figure  bounded  by 
rhree  Lines  ;  as  ABC.  Fig.  9. 

32.  An  Equilateral  Triangle  has  its  three 
aides  equal  in  length  to  each  other.  Fig.  9. 


GEOMETRY. 


33.  An  Isocles  Triangle  has  two  of  its  sides 
equal,  and  the  other  longer  or  shorter.  Fig.  10. 


Fig.  11. 


34.  A  Scalene  Triangle  has  three  unequal 
sides.     Fig.  11. 


35.  A  Right  Angled  Triangle  has  one 
Right  Angle.     Fig.  12. 


Fig.  12. 


Fig.  13. 


36.  An  Obtuse  Angled  Triangle  has  one 
Obtuse  Angle.     Fig.  13. 


37.  An  Acute  Angled  Triangle  has  all  its  Angles  Acute, 
Fig.  9,  er  10. 

38.  Acute  and  Obtuse  Angled  Triangles  are  called  Oblique 
Angled  Triangles,  or  simply  Oblique  Triangles  ;  in  which  the 
bottom  Side  is  generally  called  the  Base  and  the  other  two. 
Legs. 

39.  In  a  Right  Angled  Triangle  the  longest  side  is  called  the 
Hypothenuse,  and  the  other  two,  Legs,  or  Base  and  Perpen- 
dicular. 

Note.  The  three  Angles  of  every  Triangle  being  added  to- 
gether will  amount  to  180  Degrees ;  consequently  the  two 
Acute  Angles  of  a  Right  Angled  Triangle  amount  to  90 
Degrees,  the  Right  Angle  being  also  90* 
CJ 


14 


GEOMETRY. 


40.  The  perpendicular  height  of  a  Trfen- 
gle  is  a  Line  drawn  from  one  of  the  Angles 
to  its  opposite  side ;  thus,  the  dotted  Line 
AD.  Fig.  14.  is  the  perpendicular  height  of 
the  Triangle  ABC. 


JVbte.  This  Perpendicular  may  be  drawn  from  either  of  the 
Angles  ;  and  whether  it  falls  within  the  Triangle,  or  on 
one  of  the  Lines  continued  beyond  the  Triangle,  is  imma- 
terial. 


4K  A  Square  is  a  Figure  bounded  by  four 
equal  sides,  and  containing  four  Right  Angles. 
Fig.  15. 


42.  A  Parallelogram,  or  Oblong  Square,  is 
a  Figure  bounded  by  four  sides,  the  opposite 
ones  being  equal  and  the  Angles  Right.  Fig. 


Fig.  15. 


Fig.  16. 


Fig.  17. 


43.  A  Rhombus  is  a  Figure  bounded  by 
four  equal  sides,  but  has  its  Angles  Oblique. 
Fig.  17. 


B 


Fig.  18. 


44.  A  Rhomboides  is  a  Figure  bound- 
ed by  four  sides,  the  opposite  ones  being 
equal,  but  the  Angles  Oblique.  Fig.  18. 


GEOMETRY.  15 

45.  The  perpendicular  height  of  a  Rhombus  or  Rhomboides 
is  a  Line  drawn  from  one  of  the  Angles  to  its  opposite  side : 
thus,  the  dotted  Lines  AB.  Fig.  17.  and  Fig.  18.  represent  the 
perpendicular  height  of  the  Rhombus  and  Rhomboides. 

Fig.  19. 


46.  A  Trapezoid  is  a  Figure  bounded  by 
lour  sides,  two  of  which  are  parallel  though 
of  unequal  lengths.  Fig.  19.  and  Fig.  20. 


CH7 


Fig.  20. 

Note.  Fig.  19.  is  sometimes  called  a  Right  Angled  Trape- 
zium. 


Fig.  21, 


47.  A  Trapezium  is  a  figure  bounded  by 
four  unequal  sides.     Fig.  21. 

48.  A  Diagonal  is  a  Line  drawn  between 
two  opposite  Angles ;  as  the  Line  AB.    Fig. 
21. 


49.  Figures  which  consist  of  more  than  four  sides  are  called 
Polygons  ;  if  the  sides  are  equal  to  each  other  they  are  called 
regular  Polygons,  and  are  sometimes  named  from  the  number 
of  their  sides,  as  Pentagon,  or  Hexagon,  a  Figure  of  five  or  six 
sides,  &c.  ;  if  the  sides  are  unequal,  they  are  called  irregulav 
Polygons. 


PART  II. 

Geometrical  Problems. 


PROBLEM  I.   To  draw  a  Line  parallel  to 
another  Line  at  any  given  distance  ;  as  at  the  >;.--"-»^ 
Point  D,  to  make  a  Line,  parallel  to  the  Line 


Fig.  22. 


Fig.  22, 


- 


i; 


Jg  GEOMETRY 

With  the  Dividers  take  the  nearest  distance  between  the 
Point  D  and  the  given  Line  AB ;  with  that  distance  set  one 
foot  of  the  Dividers  any  where  on  the  Line  AB,  as  at  E,  and 
draw  the  Arch  C  ?  through  the  Point  D  draw  a  Line  so  as  just 
to  touch  the  top  of  the  Arch  C. 

A  more  convenient  way  to  draw  parallel  Lines  is  with  ;i 
parallel  Rule.  :-fc¥&V1 

Fig.  23. 


PROBLEM  II.  To  bisect  a  given  Line; 
or  to  find  the  middle  of  it.     Fig.  23. 


$?* 

Open  the  Dividers  to  any  convenient  distance,  more  than 
half  the  given  Line  AB,  and  with  one  foot  in  A,  describe  an 
Arch  above  and  below  the  Line,  as  at  C  and  D  ;  with  the  same 
distance,  -and  one  foot  in  B,  describe  Arches  to  cross  the  former ; 
lay  a  Rule  from  C  to  D,  and  where  the  Rule  crosses  the  Line, 
as  at  E,  will  be  the  middle. 

Fig.  24. 


PROBLEM  III.  To  erect  a  Perpendicular 
from  the  end,  or  any  part  of  a  given  Line.  Fig. 
24. 


m 


Open  the  Dividers  to  any  convenient  distance,  as  from  D  to 
A,  and  with  one  foot  on  the  Point  D,  from  which  the  Perpen- 
dicular is  to  be  erected,  describe  an  Arch,  as  AEG ;  set  off  the 
same  distance  from  A  to  E,  and  from  E  to  G  ;  upon  E  and  G 
describe  two  Arches  to  intersect  each  other  at  H ;  draw  a 
Line  from  H  to  D,  and  one  Line  will  be  perpendicular  to  the 
other. 

JVbfe.  There  are  other  methods  of  erecting  a  Perpendicular, 
but  this  is  the  most  simple. 


GEOMETRY,  17 

Fig.  25. 
C 


PROBLEM  IV.  From  a  given  Point, 
as  at  (',   to  drop  a  Perpendicular  on  a&. 
given  Line  AB.  Fig.  25. 


With  one  foot  of  the  dividers  in  C  describe  an  Arch  to  cut 
the  given  Line  in  two  places,  as  at  F  and  G  ;  upon  F  and  G 
describe  two  Arches  to  intersect  each  other  below  the  Line  as 
at  D  ;  lay  a  Rule  from  C  to  D  and  draw  a  Line  from  C  to  the 
given  Line. 

Perpendiculars  may  be  more  readily  raised  and  let  fall,  by  a 
small  Square  made  of  brass,  ivory,  or  wood. 

Fig.  26. 


PROBLEM  V.  To  make  an  Angle  at 
*qiial  to  a  given  Angle  ABC.  Fig.  26. 


HI 

Open  the  dividers  to  any  convenient  distance,  and  with  one 
foot  in  B  describe  the  Arch  FG  ;  with  the  same  distance  and 
one  foot  in  E,  describe  an  Arch  from  H  ;  measure  the  Arch  FG, 
and  lay  off  the  same  distance  on  the  Arch  from  H  to  I ;  draw 
a  Line  through  I  to  E,  and  the  Angles  will  be  equal. 

Fig.  27. 


PROBLEM  VI.  To  make  an  Acute  Jingle  f 
equal  to  a  given  number  of  Degrees,  suppose  f 
36.  Fig.  27.  I 

A    C 

Draw  the  Line  AB  to  any  convenient  length  ;  from  a  Scale 
of  Chords  take  60  Degrees  with  the  dividers,  and  with  one  foot 
in.  B  describe  an  Arch  from  the  Line  AB ;  from  the  same  Scale 
take  the  given  number  of  Degrees,  36,  and  lay  it  on  the  Arch 
from  C  to  D  ;  draw  a  line  from  B  through  D,  and  the  Angle  at 
B  will  be  an  Angle  of  36  Degrees. 

D 


18  GEOMETRY. 

Fig.  26, 


PROBLEM  VII.  To  make  an  Obtuse  Jin-  "  * 
'c,  suppose  of  110  Degrees.  Fig.  28. 

"~B 

Take  a  Chord  of  60  Degrees  as  before,  and  describe  an  Arch 
greater  than  a  Quadrant ;  set  off  90  Degrees  from  B  to  C,  and 
from  C  to  E  set  off  the  excess  above  90,  which  is  20  ;  draw  a 
Line  from  G  through  E,  and  the  Angle  will  contain  110  De- 
grees. 

Note.  In  a  similar  manner  Angles  may  be  measured  ;  that  is. 
with  a  Chord  of  60  Degrees  describe  an  Arch  on  the  an- 
gular Point,  and  on  a  Scale  of  Chords  measure  the  Arch 
intercepted  by  the  Lines  forming  the  angle. 

A  more  convenient  method  of  making  and  measuring  Angles 
is  to  use  a  Protractor  instead  of  a  Scale  and  Dividers. 

Fig.  29. 

B ^ O 

X 

PROBLEM  VIII.  To  make  a  Triangle  oj 
three  given  Lines,  as  BO,  BL,  LO.  Fig.  29. 


Draw  the  Line  BL  from  B  to  L  ;  from  B,  with  the  length  of 
the  Line  BO,  describe  an  Arch  as  at  O  ;  from  L,  with  the 
length  of  the  Line  LO,  describe  another  Arch  to  intersect  the 
former  ;  from  O  draw  the  Lines  OB  and  OL,  and  BOL  will  be 
the  Triangle  required. 


Fig.  30. 


PROBLEM  IX.  To  make  a  Right  Jingled 
Triangle,  the  Hypothenuse  and  Jingles  being 
«hen.  Fig.  30. 


Suppose  the  Hypothenuse  CA  25  Rods  or  Chains,  the  angl* 


GEOMETRY. 


19 


at  C  35°  3Q'  and  consequently  the  Angle  at  A  54°  30'. 
Note  after  the  39th  Geometrical  Definition. 


See 


Note.  When  degrees  and  minutes  are  expressed,  they  are 
distinguished  from  each  other  by  a  small  cipher  at  the 
right  hand  of  the  degrees,  and  a  dash  at  the  right  hand  of 
the  minutes  ;  thus  35°  30'  is  35  degrees  and  30  minutes. 

Draw  the  Line  CB  an  indefinite  length ;  at  C  make  an  Angle 
of  35°  30' ;  through  where  that  number  of  Degrees  cuts  the 
Arch  draw  the  Line  CA  25  Rods,  which  must  be  taken  from 
some  Scale  of  equal  parts  ;  drop  a  Perpendicular  from  A  to  B, 
and  the  Triangle  will  be  completed. 

Note.  The  length  of  the  two  Legs  may  be  found  by  mea- 
suring them  upon  the  same  scale  of  equal  parts  from  which 
the  Hypothenuse  was  taken. 


PROBLEM  X.  To  make  a  Right  Jin- 
gled Triangle,  the  Jingles  and  one  Leg  being 
given.  Fig.  31. 


C 


285 

Suppose  the  Angle  at  C  33°  15',  and  the  Leg  AC  285. 

Draw  the  Leg  AC  making  it  in  length  285  ;  at  A  erect  a  Per- 
pendicular an  indefinite  length ;  at  C  make  an  Angle  of  33° 
15';  through  where  that  number  of  Degrees  cuts  the  Arch, 
draw  a  Line  till  it  meets  the  Perpendicular  at  B. 

Note.  If  the  given  Line  CA  should  not  be  so  long  as  the 
Chord  of  60°,  it  may  be  continued  beyond  A,  for  the  pur- 
pose of  making  the  Angle. 

Fig.  32. 

C 


PROBLEM  XI.  To  make  a  Right  Angled 
Triangle,  the  Hypothenuse  and  one  Leg  being 
given.  Fig.  32. 


Suppose  the  Hypothenuse  AC  40,  and  the  Leg  AB  28. 

Draw  the  Leg  AB  in  length  28  ;  from  B  erect  a  Perpendi- 

qular  an  indefinite  length ;  take  40  in  the  Dividers,  and  setting 


20  GEOMETRY. 

one  foot  in  A,  wherever  the  other  foot  strikes  the  Perpendicular 
will  be  the  point  C. 

JVbte.  When  the  Triangle  is  constructed,  the  Angles  maybe 
measured  by  a  Protractor,  or  by  a  Scale  of  Chords. 

Fig.  33. 

C 


\&3$p&3  *&?**»** 

PROBLEM  XII.  To  make  a  Right  Jingled 
Triangle,  the  two  Legs  being  given.  Fig.  33. 


Suppose  the  Leg  AB  38,  and  the  Leg  BC  46. 
Draw  the  Leg  AB  in  length  38  ;  from  B  erect  a  Perpendicu- 
lar to  C  in  length  46 ;  and  draw  a  Line  from  A  to  C. 

Fig.  34. 


PROBLEM    XIII.      To 

make  an  Oblique  Jingled  Tri- 
angle, the  Jingles  and  one  Side 
being  given.  Fig.  34. 

•g  XWJTJ 

98 

Suppose  the  side  BC  98 ;  the  Angle  at  B  45O  15',  the  Angle 
at  D  108°  30',  consequently  the  other  Angle  26°  IS''. 

Draw  the  side  BC  in  length  98 ;  on  the  Point  B  make  an  An- 
gle of  450  15' ;  on  the  Point  C  make  an  Angle  of  26O  15',  and 
draw  the  Lines  BD  and  CD. 

Fig.  35. 

I) 

PROBLEM  XIV.  To  make  an  Oblique 
Angled  Triangle,  two  Sides  and  an  Jingle  op- 
posite  to  one  of  them  being  given.  Fig.  35.  ._ 

±60 

Suppose  the  side  BC  160,  the  side  BD  79,  and  the  Angle  at 
C  290  9'. 

Draw  the  side  BC  in  length  160 ;  at  C  make  an  Angle  of 
29°  9',  and  draw  an  indefinite  Line  through  where  the  Degrees 
cut  the  Arch ;  take  79  in  the  dividers,  and  with  one  foot  in  B 
lay  the  other  on  the  Line  CD  ;  the  point  D  will  be  the  other 
Angle  of  the  Triangle. 


GEOMETRY. 


Fig.  36. 


PROBLEM  XV.  TomakeanOblique1*- — 
Jingled    Triangle,  two  Sides  and  their 
contained  Angle  being  given.   Fig.  36. 


Suppose  the  side  BC  109,  the  side  BD  76,  and  the  Angle  at 
B  1010  30'. 

Draw  the  side  BC  in  length  109 ;  at  B  make  an  Angle  of 
1010  30',  and  draw  the  side  BD  in  length  76  ;  draw  a  line  from 
D  to  C  and  it  is  done. 

Fig.  37. 


PROBLEM 

Fig.  37. 


XVI.      To  make  a  Square. 


Draw  the  Line  AB  the  length  of  the  proposed  Square  ;  from 
B  erect  a  Perpendicular  to  C  and  make  it  of  the  same  length  as 
AB ;  from  A  and  C,  with  the  same  distance  in  the  dividers,  de- 
scribe Arches  intersecting  each  other  at  D,  and  draw  the  Lines 
AD  and  DC. 


PROBLEM  XVII.  To  make  a  ParaUdo- 
<-am.     Fig.  38. 


Draw  the  Line  AB  equal  to  the  longest  side  of  the  Parallelo- 
gram ;  on  B  erect  a  Perpendicular  the  length  of  the  shortest 
side  to  C  ;  from  C,  with  the  longest  side,  and  from  A,  with  the 
shortest  side,  describe  Arches  intersecting  each  other  at  D,  and 
draw  the  Liues  AD  and  CD. 


E 


GEOMETRY. 


PROBLEM  XVIII.  To  describe 
a  Circle,  which  shall  pass  through 
any  three  given  Points,  not  lying  in 
a  Right  Line,  as  A,  B,  D.  Fig.  43. 


Fig.  43. 


Draw  Lines  from  A  to  B  and  from  B  to  D ;  bisect  those  Line* 
by  PROBLEM  II.  and  the  Point  where  the  bisecting  Lines  inter 
sect  each  other,  as  at  C,  will  be  the  centre  of  the  Circle. 

PROBLEM  XIX.   To  find  the  centre  of  a  Circle. 

By  the  last  PROBLEM  it  is  plain,  that  if  three  Points  be  any 
where  taken  in  the  given  Circle's  Periphery,  the  centre  of  the 
Circle  may  be  found  as  there  taught. 

Directions  for  constructing  irregular  Figures  of  four  or  more 
sides  may  be  found  in  the  following  Treatise  on  SURVEYING, 


TRIGONOMETRY. 


TRIGONOMETRY  is  that  part  of  practical  GEOMETRY  hy 
which  the  Sides  and  Angles  of  Triangles  are  measured  ;  where- 
by three  things  being  given,  either  all  sides,  or  sides  and  Angles, 
a  fourth  may  be  found ;  either  by  measuring  with  a  Scale  and 
Dividers,  according  to  the  PROBLEMS  in  GEOMETRY,  or  more 
accurately  by  calculation  with  Logarithms,  or  with  Natural 
Sines. 

TRIGONOMETRY  is  divided  into  two  Parts,  Rectangular  and 
Oblique-angular. 

PART  I. 

RECTANGULAR  TRIGONOMETRY. 

This  is  founded  on  the  following  methods  of  applying  a  Tri- 
angle to  a  Circle. 

Fig.  44. 

PROPOSITION  I.     In  every  Right  C 

Angled  Triangle,  as  ABC,  Fig.  44,  it  is 
plain  from  Fig.  7.  compared  with  the 
Geometrical  definitions  ,to  which  that 
Figure  refers,  that  if  the  Hypothenuse  A, 
AC  be  made  Radius,  and  with  it  an  Arch  \~~ 
of  a  Circle  be  described  from  each  end,     \ 
BC  will  be  the  Sine  of  the  Angle  at  A,       v 
and  AB  the  Sine  of  the  Angle  at  C  ;  that 
is,  the  Legs  will  be  Sines  of  their  oppo- 
site Angles., 

45. 

PROPOSITION  II.  If  one  Leg,  AB, 
Fig.  45,  be  made  Radius,  and  with  it  on 
the  Point  A  an  Arch  be  described,  then 
BC,  the  other  Leg,  will  be  the  Tangent 
and  AC  the  Secant  of  the  Angle  at  A  ; 
and  if  BC  be  made  Radius,  and  an  Arch 
be  described  with  it  on  the  Point  C,  then 
AB  will  be  the  Tangent  and  AC  the  Se- 
cant of  the  Angle  at  C  ;  that  is,  if  one  Leg 
be  made  Radius  the  other  Leg  will  be  a  Tangent  of  its  opposite 
Angle,  and  the  Hypothenuse  a  Secant  of  the  same  Angle. 


U  TRIGONOMETRY. 

Thus,  as  different  sides  are  made  Radius,  the  other  sides  ac- 
quire different  names,  which  are  either  Sines,  Tangents  or  Se- 
cants. 

As  the  sides  and  Angles  of  Triangles  bear  a  certain  propor- 
tion to  each  other,  two  sides  and  one  Angle,  or  one  side  and 
two  Angles  being  given,  the  other  sides  or  Angles  may  be  found 
by  instituting  Proportions,  according  to  the  following  Rules. 

RULE  I.  To  find  a  side,  either  of  the  sides  may  be  made 
Radius,  then  institute  the  following  Proportion : 

As  the  name  of  the  side  given,  which  will  be  either  Radius. 

Sine,  Tangent  or  Secant ; 
Is  to  the  length  of  the  side  given ; 
So  is  the  name  of  the  side  required,  which  also  will  be  either 

Radius,  Sine,  Tangent  or  Secant ; 
To  the  length  of  the  side  required. 

RULE  II.  To  find  an  Angle  one  of  the  given  sides  must  be 
made  Radius,  then  institute  the  following  Proportion  : 

As  the  length  of  the  given  side  made  Radius ; 

Is  to  its  name,  that  is  Radius  ; 

So  is  the  length  of  the  other  given  side ; 

To  its  name,  which  will  be  either  Sine,  Tangent  or  Secant, 

Having  instituted  the  Proportion,  look  for  the  corresponding 
Logarithms,  in  the  Logarithms  for  numbers  for  the  length  of  the 
sides,  and  in  the  Table  of  Artificial  Sines,  Tangents  and  Se- 
cants, for  the  Logarithmic  Sine,  Tangent  or  Secant. 

Having  found  the  Logarithms  of  the  three  given  Terms,  add 
together  the  Log.  of  the  second  and  third  Terms,  and  from 
their  sum  subtract  the  Log.  of  the  first  Term,  the  Remainder 
will  be  the  Log.  of  the  fourth  Term,  which,  seek  in  the  Tables 
and  find  its  corresponding  Number  or  Degrees  and  Minutes. 

See  the  Introduction  to  the  Table  of  Logarithms ;  which 
should  be  attentively  studied  by  the  Learner  before  he  proceeds 
any  further. 

Note.  The  Logarithm  for  Radius  is  always  10,  which  is  the 
Logarithmic  Sine  of  90°,  and  the  Logarithmic  Tangent  of 
450. 

The  preceding  PROPOSITIONS  and  RULES  being  duly  attendee! 
to,  the  solution  of  the  following  GASES  of  Rectangular  Tngona- 
will  be  easy. 


TRIGONOMETRY 


CASE  I. 


The  Jingles  and  Hypothenuse  given  to  find 
the  Legs.  Fig.  39. 


Fig.  39. 


In  the  Triangle  ABC,  given  the  Hypothenuse  AC  25  Rods 
or  Chains ;  the  Angle  at  A  35°  3(K :  and  consequently  the 
Angle  at  C  54°  30' :  to  find  the  Legs. 


Making  the  Hypothenuse  Radius,  the  Proportions  will  be  : 

To  find  the  Leg  EC. 
As  Radius  +»       -         10.00000 

:  Hyp.  AC,  25-    -    ...>:*      1.39794 
:  :  Sine  CAB,  35°  30'  9.76395 


To  find  the  Leg  AB. 
As  Radius  -        -        10.00000 

~  :  Hyp.  AC,  25     -        -  1.39794 

:  :  Sine  ACB,  54°  30>  9.91069 


11.30863 
10.00000 


:  Leg  AB,  20.35 


1.30863 


:  Leg  BC,  14.52 


11.16189 
10.00000 

1.16189 


JVbte.  When  the  first -Term  is  Radius,  it  may  be  subtracted 
by  cancelling  the  first  figure  of  the  Sum  of  the  other  two 
Terms. 

Making  the  Leg  AB  Radius,  the  Proportions  will  be  : 


To  find  the  Leg  AB. 
As  Secant  CAB,  35°  30' 
:  Hyp.  AC,  25 
:  :  Radius 
:  Leg  AB,  20.35 


To  find  the  Leg  BC. 
As  Secant  CAB,  35°  30' 
:  Hyp.  AC,  25 
:  :  Tangent,  CAB,  35°  30X 
:  Leg  BC,  14.52 


Making  the  Leg  BC  Radius,  the  Proportions  will  be  : 


To  find  the  Leg  AB. 
As  Secant  ABC,  54°  30' 
:  Hyp.  AC,  25 
:  :  Tangent  ACB,  54°  30' 
:LegAB,  20.35 


To  find  the  Leg  BC. 
As  Secant  ACB,  54°  30' 
:  Hyp.  AC,  25 
:  :  Radius 
:  Leg.  BC,  14.52 


The  Logarithms  of  the  four  last  Proportions  being  looked 
out,  and  added  and  subtracted  according  to  the  Rule,  the  result 
will  be  found  to  be  the  same  as  the  two  first  Proportions. 

F 


TRIGONOMETRY. 


By  Natural  Sines. 

This  CASE  may  be  solved  by  Natural  Sines,*  according  to 
the  following  Proportions  : 

As  Unity  or  1,  is  to  the  length  «f  the  Hypothenuse,  so  is  the 
Natural  Sine  of  the  smallest  Angle,  to  the  length  of  the  short- 
est Leg.  Or,  so  is  the  Natural  Sine  of  the  largest  Angle,  to 
the  length  of  the  longest  Leg. 

Or,  which  is  the  s&me  thing,  multiply  the  Natural  Sines  of 
the  two  Angles  by  the  Hypothenuse,  the  Products  will  be  the 
length  of  the  two  Legs. 

EXAMPLE. 

Nat.  Sine  of  35O  30'  Nat.  Sine  of  54°  30' 

0.58070  0.81412 

Hyp.  25  Hyp.          25 


290350  407060 

116140  162S24 


14.51750  20.35300 


Leg  BC   14.52  Leg  AB  20.35 

J\"ole.  The  third  Decimal  figure  in  the  first  Product  being  7, 
the  preceding  figure  may  be  called  one  more  than  it  is, 
vis.  2.  And  whenever  in  any  Product,  &c.  there  are  more 
places  of  Decimals  than  you  wish  to  work  with,  if  the 
one  at  the  right  hand  of  the  last  which  you  wish  to  retain 
is  more  than  5,  add  a  Unit  to  the  last,  because  a  greater 
number  than  5  is  more  than  half. 

As  the  Table  of  Artificial  or  Logarithmic  Sines,  Tangents 
and  Secants,  contained  in  this  book,  is  calculated  only  for  every 
5  Minutes  of  a  Degree,  whenever  any  Question  is  to  be  solved 
where  the  Minutes  cannot  be  found  in  that  Table  ;  or  where 
the  length  of  the  Hypothenuse  is  such  a  number  as  cannot  be 
found  in  the  Table  of  Logarithms  for  Numbers,  the  Question 
may  be  solved  by  Natural  Sines  as  above  taught. 

\ 

*  See  the  Introduction  to  the  Table  of  Natural  Sines. 


TRIGONOMETRY. 


CASE  II. 


The  Angles  and  one  Leg  given,  to  find  the 
Hypothenuse  and  the  other  Leg.  Fig.  40. 


Fig.  40, 


325 


In  the  Triangle  ABC,  given  the  Leg  AB  325,  the  Angle  at  A 
330  15X  and  the  Angle  at  C  56°  45' :  to  find  the  Hypothenuse 
and  the  Leg  BC.  - 

Making  the  given  Leg  Radius,  the  Proportions  will  be  : 


To  find  the  Hypothenuse 
As  Radius,  10.00000 

:  Leg  AB,  325  2.51188 

:  :  Sec.  CAB,  33°  15'          10.07765 


rHyp.  388.6 


12.58953 


To  find  the  Leg  BC. 
As  Radius,  10.00000 

:  Leg  AB,  325  2.511S8 

:  :  Tan.  CAB,  33°  15'  9.81666 


:  Leg  BC,  213.1 


12.32854 


Note.  Reject  the  first  figure,  which  is  the  same  as  subtract- 
ing Radius,  and  seek  the  numbers  corresponding  to  the 
other  figures. 

Making  the  Leg  BC  Radius,  the  Proportions  will  be  ; 


To  find  the  Hypothenuse 
As  Tang.  ACB,  56O  45' 
:  Leg  AB,  325 
:  :  Sect.  ACB.  56O  46' 
:  Hyp.  388.6 


To  find  the  Leg  BC. 
As  Tang.  ACB,  56O  45' 
:  Leg  AB,  325 
:  :  Radius 
:  LegBC,  213.1 


Making  the  Hypothenuse  Radius,  the  Proportions  will  be  ; 

To  find  the  Leg  BC. 


To  find  the  Hypothenuse. 
As  Sine  BCA,  56°  45' 
:  Leg  AB,  325 
:  :  Radius 
:  Hyp.  388.6 


As  Sine  BCA,  56°  45' 
:LegAB,  325 
:  :  Sine  BAC,  33°  15' 
:  Leg  BC,  213. 


Note.  If  the  Leg  BC  had  been  given,  instead  of  the  Leg  AB? 
the  Proportions  would  have  been  the  same  mutatis  mutan- 
dis. 


By.  Natural  Sine*. 

To  sol*e  this  CASE  by  Natural  Sines,  institute  the  following 
Proportions  : 


28  TRIGONOMETRY. 

To  find  the  Hypothenuse.  As  the  Natural  Sine  of  the  Angle 
opposite  the  given  Leg,  is  to  the  length  of  the  Leg,  so  is  Unity 
or  1,  to  the  length  of  the  Hypothenuse. 

Or,  which  is  the  same  thing,  D'ivide^the  given  Leg  by  the 
Natural  Sine  of  its  opposite  Angle,  and  the  Quotient  will  he 
the  Hypothenuse. 

To  find  the  other  Leg.  As  the  Natural  Sine  of  the  Angle  op- 
posite the  given  Leg,  is  to  the  length  of  the  given  Leg,  so  is  the 
Natural  Sine  of  the  Angle  opposite  the  other  Leg,  to  the  length 
of  the  other  Leg. 

EXAMPLE. 

Given  Leg  325.  Nat.  Sine  of  56°  45',  the  Angle  opposite 
the  given  Leg  0.83629.  Nat.  Sine  of  33°  15',  the  Angle  op- 
posite the  other  Leg  0.54829. 

As  0.83629  :.325  :  :  1  :  388.6 

As  0.83629  :  325  :  :  0.54829  :  213.07. 


CASE  III. 


The  Hypothenuse  and  one  Leg  gtven,  to  find 
the  Jingles  and  the  other  Leg.  Fig.  41.     ,  >•• 


In  the  Triangle  ABC,  given  the  Hypothenuse  AC  50  and  the 
Leg  AB  40,  to  find  the  Angles  and  Leg  BC. 

Making  the  Hypothenuse  Radius,  the  Proportion  to  find  the 
Angle  ACB  will  be  : 

As  Hyp.  50  1.69897 

:  Radius  10.00000 

::LegAB,  40   ^  -  1.60206 


11.60206 
1.69897 

:  Sine  ACB,  53°  10'          9.90309 


The  Angle  ACB  being  53°  10'  the  other  is  consequently 
360  50'. 


HI  TRIGONOMETRY,  29 

Making  the  Leg  AB  Radius,  tfee  Angle<?BAC  may  be  found  by 
the  following  Proportion ; 

As  Leg  AB,  40       ..  -        1.60206 

:  Radius          -  ..W>a     1O.OOOOO 

.     : :  Hyp.  50     -         -  1.69897 


11.69897 
1.60206 


:  Sec.  BAC,  360  50'         10.09691 

The  Angles  being  found,  the  Leg  BC  maybe  found  by  either 
the  preceding  CASES.     It  is  30. 


By  Natural  Sines. 

The  Angle  opposite  the  given  Leg  may  be  found  by  the  fol- 
lowing Proportion ; 

As  the  Hypothenuse  is  to  Unity  or  1,  so  is  the  given  leg  to 
the  Nat.  Sine  of  its  opposite  Angle. 

Or,  which  is  the  same  thing,  Divide  the  given  Leg  by  the 
Hypothenuse,  and  the  Quotient  will  be  the  Nat.  Sine. 

EXAMPLE. 

The  Leg  AB  40  divided  by  the  Hypothenuse  50  quotes 
0,80000  which  looked  in  the  Table  of  Nat.  Sines,  the  nearest 
corresponding  number  of  Degrees  and  Minutes  will  be  found 
to  be  530  8X,  the  Angle  AC B. 

JVofe.  The  reason  why  the  Angle  as  found  by  Nat.  Sines 
differs  2  Minutes  from  the  Angle  as  found  by  Logarithms, 
is  that  the  Table  of  Logarithmic  Sines,  &c.  contained  in 
this  book,  is  calculated  only  for  every  5  minutes.  By  a 
Table  of  Logarithmic  Sines,  &c.  calculated  for  every 
minute^  the  Ajigle  will  be  found  the  same. 


By  the  Square  Root. 

In  this  CASE  the  required  Leg  may  be  found  by  the  Square 
Root,  without  finding  the  Angles ;  according  to  the  following 
PROPOSITION  ; 

G 


SO  TRIGONOMETRY, 

In  every  Right  Angled  Triangle,  the  Square  of  the  Hypo- 
thenuse  is  equal  to  the  Sum  of  the  Squares  of  the  two  Legs. 
Hence, 

The  Square  of  the  given  .Leg  being  subtracted  from  the 
Square  of  the  Hypothenuse,  the  Remainder  will  be  the  Square 
of  the  required  Leg. 

As  in  the  preceding  EXAMPLE  ;  the  Square  of  the  Leg  AB  40 
is  1600  ;  this  subtracted  from  the  Square  of  the  Hypothenuse 
50  which  is  2500,  leaves  900,  the  Square  of  the  Leg  BC,  the 
Square  Root  of  which  is  30,  the  length  of  Leg  BC  as  found  by 
Logarithms; 


CASE  IV; 

Fig.  42. 


The  Legs  given  to  find  the  Jingles  and  Hy 
pothemtsc.     Fig.  42. 


78.T 


In  the  Triangle  ABC,  given  the  Leg  AB  78.7  and  the  Leg 
BC  b9  ;  to  find  the  Angles  and  Hypothenuse. 

Making  the  Leg  AB  Radius,  the  Proportion  to  find  the  Angle 
BAC  will  be ; 

As  Leg  AB,  78.7  1.89597 

:  Radius  2'ii:*     10.00000 

r:  Leg  BC,  89       A    <       1.94939 


11.94939 
1.89597 


:  Tang.  BAC,  48O  3(K     10.05342 


The  Angle  ACB  is  consequently  410  30'. 

Making  the  Leg  BC  Radius,  the  Proportion  to  find  the  Angle 
BCA  will  be  the  same  as  the  above,  mutatis  inutandis. 

The  Angles  being  found,  the  Hypothenuse  may  be  found  lw 
CASE  IL  It  is  nearest  119. 


TRIGONOMETRY. 

By  the  Square  Root, 


la  this  Case  the  Hypothenuse  may  be  found  by  the  Square 
Root,  without  finding  the  Angles  ;  according  to  the  following 
PROPOSITION. 

In  every  Right  Angled  Triangle,  the  sum  of  the  Squares  of 
the  two  Legs  is  equal  to  the  Square  of  the  Hypothenuse. 

In  the  above  EXAMPLE,  the  Square  of  AB  78.7  is  6193.69, 
the  Square  of  BC  89  is  7921  ;  these  added  make  14114.69  the 
Square  Root  of  which  is  nearest  119. 


By  Natural  Sines. 

The  Hypothenuse  being  found  by  the  Square  Root,  the  Angles 
may  be  found  by  Nat.  Sines,  according  to  the  preceding  CASE, 
Hyp.    Leg.  BC.         Nat.  Sine. 
119)    89.00000  (74789 
833 

570  The  nearest  degrees  and  minutes  cor- 

476  responding  to  the  above  Nat.  Sine  are  48^ 

24',  for  the  Angle  BAC.     The  difference 

940  between  this  and  the  Angle  as  found  by 

833  Logarithms  is  occasioned  by  dividing  by 

119,  which  is  not  the  exact  length  of  the 

1070  Hypothenuse,  it  being  a  Fraction  too  much, 
952 

1180 
1071 

109 


PART  II. 

OBLIQUE  TRIGONOMETRY. 

The  solution  of  the  two  first  CASES  of  Oblique  Trigonometry 
cfepends  on  the  following  PROPOSITION. 

In  all  Plane  Triangles,  the  Sides  are  in  proportion  to  each 
other  as  the  Sines  of  their  opposite  Angles.  That  is,  as  tire- 


32  TRIGONOMETRY. 

Sine  of  one  Angle  is  to  its  opposite  Side,  so  is  the  Sine  of  an- 
other Angle  to  its  opposite  Side.  Or,  as  one  Side  is  to  its  oppo- 
site Angle,  so  is  another  Side  to  the  Sine  of  its  opposite  Angle.-, 

JYbfc.  When  an  Angle  exceeds  90°  make  use  of  its  Supple- 
ment, which  is  what  it  wants  of  180°.  As  the  Sine  of  90° 
is  the  greatest  possible  Sine,  the  Sine  of  any  number  of 
Degrees  will  be  as  much  less  as  .that  number  of  Degrees^, 
exceeds  90,  and  will  be  the  same  as  the  Sine  of  the  Sup- 
plement of  that  number  of  Degrees ;  thus,  the  Sine  of 
100°  is  the  same  as  the  Sine  of  80°,  and  the  Sine  of  130C 
the  same  as  the  Sine  of  50°,  &c. 


CASE  I, 


Fig.  47. 

c 


Ilie  Jingles  and  one  Side  given,  to  find  the 
other  Sides.     Fig.  47. 


In  the  Triangle  ABC,  given  the  Angle  at  B  48°,  the  Angle 
at  C  72°,  consequently  the  Angle  at  A  60°,  and  the  Side  AB 
200,  to  find  the  Sides  AC  and  BC. 


To  find  the  Side  AC. 
As  Sine  ACB,  72°        -        9.97821 
:  Side  AB,  200      -.        -        2.30103 
t :  Sine  ABC,  48°          -.        9.87107 


Side  AC,  156     - 


12.17210 
9.97821 

2.19389 


To  find  the  Side  BC. 
As  Sine  ACB,  73Q         -        9.97821 
:  Side  AB,  200      -        -        2.30103 
:  :  Sine  BAG,  60°      •    ~  ,-    9.93753 


:  Side  BC,  182      - 


12.32856 
9.97821 

2.26036 


By  Natural  Sines. 

As  the  Nat.  Sine  of  the  Angle  opposite  the  given  Side  is  to 
the  given  Side,  so  is  the  Nat.  Sine  of  the  Angle  opposite  either 
of  the  required  Sides  to  that  required  Side. 


TRIGONOMETRY. 


Side  200 ;   Nat.   Sine  of  72°,  its  opposite  Angle* 

T^T       *         *"!•  /»       A    •»•»./•*        .  »•*•          *    ,-- . 


Given 

0.95115  ;  Nat.  Sine  of  ABC  48°,  0.74334 ;  NaV  Sine  of  BAG 
600,  0.86617. 

As  0.95115  :  200  : :  0.74334  :  156 

As  0.95115  :  200  :  :  0.86617  :  182. 


CASE  II. 


Two  Sides,  and  an  Angle 
them  given,  to  find  the  other 
Fig.  48. 


mte  to  one  of 
des  and  Side. 


In  the  Triangle  ABC,  given  the  Side  AB  240,  the  Side  BC 
200,  and  the  Angle  at  A  46°  30' ;  to  find  the  other  Andes  and 
the  Side  AC. 

To  find  the  Jlnglt  ACB. 
As  Side  BC,  200  2.30103 


Sine  BAG,  46°  30' 
:  Side  AB,  240 


Sine  ACB,  60°  30' 


9.86056 
2.38021 

12.24077 
2.30103 

9.93974 


Angle  at  A 
C 


Sum  of  the  three  Angles 
Sum  of  two 


46°  30' 
6030 

107.00 

180° 
107 


Angle  at  B  73 

The  Side  AC  will  be  found  by  CASE  I.  to  be  nearest  253. 

If  the  given  Angle  be  Obtuse,  the  Angle  sought  will 
be  Acute  ;  but  if  the  given  Angle  be  Acute,  and  opposite 
a  given  lesser  Side,  then  the  Angle  found  by  the  operation 
may  be  either  Obtuse  or  Acute.  It  ought  therefore  to  be 
mentioned  which  it  is,  by  the  conditions  of  the  question. 


By  Natural  Sines. 

As  the  Side  opposite  the  given  Angle  is  to  the  Nat.  Sine  of 
that  Angle,  so  is  the  other  given  Side  to  the  Nat.  Sine  of  its 
opposite  Angle. 

One  given  Side  200,  Nat.  Sine  of  46°  30',  its  opposite  Angle, 
0.72537,  the  other  given  Side  240. 

As  200  :  0.72537  : ;  240  :  0.87044=60°  30'. 

H 


34  TRIGONOMETRY. 

CASE  III. 


Ttoo  Sides  and  their  contained  Angle  given, 
to  find  the  other  Jingles  and  Side.     Fig.  49. 


The  solution  of  this  CASE  depends  on  the  following  PROPO- 
SITION. 

In  every  Plane  Triangle,  as  the  sum  of  any  two  Sides  is  to 
their  difference,  so  is  the  Tangent  of  half  the  sum  of  the  two 
opposite  Angles  to  the  Tangent  of  half  the  difference  between 
them.  Add  this  half  difference  to  half  the  sum  of  the  Angles 
and  you  will  have  the  greater  Angle,  and  subtract  the  half  dif- 
ference from  the  half  sum  and  you  will  have  the  lesser  Angle. 

In  the  Triangle  ABC,  given  the  Side  AB  240.,  the  Side  AC 
180,  and  the  Angle  at  A  36°  40'<-to-  find  the  other  Angles  and 
Side. 

SideAB  240  AB  240 

AC  ;'*'  180  AC  180  , 

Sum  of  the  two  Sides        420  Difference  60 

The  given  Angle  BAC  36°  40',  subtracted  from  180°,  leaves 
143°  20'  the  sum  of  the  other  two  Angles,  the  half  of  which  is 
71°  40'. 

As  the  sum  of  two  Sides,  420  '<  V.JL^         2.62325 

:  Their  difference  60  **>  «.;         1.77815 

N  ':  :  Tangent  half  unknown  Ang.  71°  40'  10.47969 


12.25784 
2.62325 

-Tangent  half  difference,  23°  2(X  9.63459 

The  half  sum  of  the  two  unknown  Angles,  71°  40' 

The  half  difference  between  them,  23  20 


Add,  gives  the  greater  Angle  ACB  95  00 


Subtract,  gives  the  lesser  Angle  ABC  48  20 

\  -__ 

The  Side  BC  may  be  found  by  CASE  I  or  II. 


TRIGONOMETRY. 


CASE  IV. 


The  three  Sides  given  to  find  the 
%les.  Fig.  50. 


A       105        U         B 

The  solution  of  this  CASE  depends  on  the  following  PROPO- 
SITION. 

In  every  Plane  Triangle,  as  the  longest  Side  is  to  the  sum 
of  the  other  two  Sides,  so  is  the  difference  between  those  two 
Sides  to  the  difference  between  the  Segments  of  the  longest 
Side,  made  by  a  Perpendicular  let  fall  from  the  Angle  opposite 
that  Side. 

Half  the  difference  between  these  Segments,  added  to  half 
the  sum  of  the  Segments,  that  is,  to  half  the  length  of  the 
longest  Side,  will  give  the  greatest  Segment ;  and  this  half  dif- 
ference subtracted  from  the  half  sum  will  be  the  lesser  Seg- 
ment. The  Triangle  being  thus  divided,  becomes  two  Right 
Angled  Triangles,  in  which  the  Hypothenuse  and  one  Leg  are 
given  to  find  the  Angles. 

In  the  Triangle  ABC,  given  the  Side  AB  105,  the  Side  AC 
85,  and  the  Side  BC  50,  to  find  the  Angles. 

Side  AC  -  85  AC  85 

BC  -  50  BC  50 


Sum  of  the  two  Sides       135 

As  the  longest  Side  AB,  105 
:  Sum  of  the  other  two  Sides,  135 
:  :  Difference  between  those  Sides,  35 


Difference  between  the  Segments,  45 

Half  the  Side  AB 

Half  the  difference  of  the  Segments 

Add,  gives  the  greater  Segment  AD 
Subtract,  gives  the  lesser  Segment  BD 


Difference 


35 

2.02119 
2.13033 
1.54407 

3.67440 
2.0211$ 

1.65321 

52.5 
22.5 

75.0 
30,0 


TRIGONOMETRY. 


Thus  the  Triangle  is  divided  into  two  Right  Angled  Trian- 
gles, ADC  and  BDC  ;  in  each  of  which  the  Hypothenuse  and 
one  Leg  are  given  to  find  the  Angles. 

To  find  the  Jingle  DCA. 
As  Hyp.  AC,  85  -         1.92942 

:  Radius         -        -        -       10.00000 
:  :  Seg.  AD,  75      -        -         1.87506 


Sine  DCA,  61°  55' 


11.87506 
1.92942 

9.94564 


To  find  the  Angle  DCB. 
As  Hyp.  BC,  50  -        1.69897 

:  Radius        -        -         -       10.00000 
: :  Seg.  BD,  30     -        ^        1.47712 


:  Sine  DCB,  36°  50 


11.47712 

1.69897 

9.77815 


The  Angle  DCA  61Q  55'  subtracted  from  9(P  leaves  the 
Angle  CAD  28O  5'. 

The  Angle  DCB  36°  50'  subtracted  from  90°  leaves  the  An- 
gle CBD  530  10'. 

The  Angle  DCA  61°  55' added  to  the  Angle  DCB  36°  50 
gives  the  Angle  ACB  98°  45'. 

This  Case  may  also  be  solved  according  to  the  following 
PROPOSITION. 

In  every  Plane  Triangle,  as  the  Product  of  any  two  Sides 
containing  a  required  Angle  is  to  the  Product  of  half  the  sum 
of  the  three  Sides,  and  the  difference  between  that  half  sum 
and  the  Side  opposite  the  Angle  required,  so  is  the  Square  of 
Radius  to  the  Square  of  the  Co-Sine  of  half  the  Angle  re- 
quired. 


Those  who  make  themselves  well  acquainted  with  TRIGONO- 
METRY will  find  its  application  easy  to  many  useful  purposes, 
particularly  to  the  mensuration  of  Heights  and  Distances  ; 
called  ALTIMETRY  and  LONGIMETRY.  These  are  here  omitted, 
because,  as  this  work  is  designed  principally  to  teach  the  Art 
of  common  FIELD-SURVEYING,  it  was  thought  improper  to  swell 
its  size,  and  consequently  increase  its  price,  by  inserting  any 
thing  not  particularly  connected  with  that  Art. 

It  is  recommended  to  those  who  design  to  be  Surveyors  to 
study  TRIGONOMETRY  thoroughly  ;  for  though  a  common  field 
may  be  measured  without  an  acquaintance  with  that  Science, 
yet  many  cases  will  occur  in  practice  where  a  knowledge  of  it 
will  be  found  very  beneficial ;  particularly  in  dividing  Land, 
and  ascertaining  the  boundaries  of  old  Surveys.  Indeed  no 
one  who  is  ignorant  of  TRIGONOMETRY,  can  be  an  accomplished 
Surveyor. 


SURVEYING. 


SURVEYING  is  the  Art  of  measuring,  laying  Out,  and  di- 
viding Land. 

PART  I. 

MEASURING  LAND. 

The  most  common  measure  for  Land  is  the  Acre ;  which 
c0Utains  160  Square  Rods,  Poles  or  Perches ;  or  4  Square 
Roods,  each  containing  40  Square  Rods. 

The  instrument  most  in  use,  for  measuring  the  Sides  of  Fields., 
is  GUNTER'S  Chain,  which  is  in  length  4  Rods  or  66  Feet ;  and 
ia  divided  into  100  equal  parts,  called  Links,  each  containing  7 
Inches  and  92  Hundredths.  Consequently,  1  Square  Chain 
contains  16  Square  Rods,  and  10  Square  Chains  make  1  Acre. 

In  small  Fields,  or  where  the  Land  is  uneven,  as  is  the  ease 
with  a  great  part  of  the  Land  in  New-England,  it  is  better  to 
use  a  Chain  of  only  two  Rods  in  length  ;  as  the  Survey  can  be 
mqre  accurately  taken. 


SECTION  I. 

PRELIMINARY  PROBLEMS. 

PROBLEM  I.  To  reduce  Two  Rod  Chains  to  Four  Hod 
CJiains. 

RULE.  If  the  number  of  Two  Rod  Chains  be  even,  take 
half  the  number  for  Four  Rod  Chains,  and  annex  the  Links  if 
any  :  thus,  16  Two  Rod  Chains  and  37  Links  make  8  Four. 
Rod  Chains  and  37  Links. 

But  if  the  number  of  Chains  be  odd,  take  half  the  greatest 
eyeri  number  for  Chains,  and  for  the  remaining  number  add  50 
to  the  Links  :  Thus,  17  Two  Rod  Chains  and  42  Links  make 
S.  Four  Rod  Chains  and  92  Links. 

PROBLEM  II.  To  reduce  Two  Rod  Chain*  to  Rods  and 
Dctin.fl  Parts. 

I 


3fc  SURVEYING. 

RULE.  Multiply  the  Chains  by  2,  and  the  Links  by  4,  which 
will  give  Hundredths  of  a  Rod  :  thus,  17  Two  Rod  Chains  and 
21  Links  make  34  Rods  and  84  Hundredths  ;  expressed  thus, 
34.84  Rods. 

If  the  Links  exceed  25,  add  1  to  the  number  of  Rods  and 
multiply  the  excess  by  4  :  thus,  15  Two  Rod  Chains  and  38 
Links  make  31.52  Rods. 

PROBLEM  III.  To  reduce  Four  Rod  Chains  to  Rods  (and 
Decimal  parts. 

RULE.  Multiply  the  Chains,  or  Chains  and  Links,  by  4 ; 
the  Product  will  be  Rods  and  Hundredths  :  thus,  8  Chains  and 
64  Links  make  34.56  Rods. 

Note.  The  reverse  of  this  Rule,  that  is,  dividing  by  4,  will  reduce  Rods 
and  Decimals  to  Chains  and  Links  :  thus,  105.12  Rods  make  26  Chains 
and  28  Links. 

PROBLEM  IV.     To  reduce  Square  Rods  to  Acres. 

RULE.  Divide  the  Rods  by  160,  and  the  Remainder  by  40, 
]f  it  exceeds  that  number,  for  Roods  or  Quarters  of  an  Acre  : 
thus,  746  Square  Rods  make  4  Acres,  2  Roods,  and  26  Rods. 

PROBLEM  V.     To  reduce  Square  Chains  to  Acres. 

RULE.  Divide  by  10  ;  or,  which  is  the  same  thing,  cut  oft' 
the  Right  hand  figure  :  thus,  1460  Square  Chains  make  14tj 
Acres  ;  and  846  Square  Chains  make  84  Acres  and  6  Tenths- 

PROBLEM  VI.     To  reduce  Square  Links  to  Acres. 

RULE.  Divide  by  100000 ;  or,  which  is  the  same  thing,  cut 
off  the  5  Right-hand  figures  :  thus,  3845120  Square  Links  make1 
38  Acres  and  45120  Decimals. 

JVofe.  When  the  Area  of  a  Field,  by  which  is  meant  its  Superficial  Con- 
tents, is  expressed  in  Square  Chains  and  Links,  the  whole  may  be  consi- 
dered as  Square  Links,  and  the  number  of  Acres  contained  in  the  Field, 
found  as  above.  Then  multiply  the  figures  cut  off  by  4,  and  again  cut 
off  5  figures,  and  you  have  the  Roods  ;  multiply  the  figures  last  cut  eft 
by  40,  and  again  cut  off  5  figures,  and  you  have  the  Rod's. 

EXAMPLE.  How  many  Acres,  Roods,  arid  Rods,   are  there  in  156 
Square  Chains  and  3274  Square  Links  ? 

15)63274  Square  Links, 
4 

2)53096 
40 

21)23840 


Answer.    15  Acres  2  Roods  and  21  Rods. 


PROBLEMS  for  finding  the  Area  of  Right  Lined  Figures,  and 
also  of  Circles. 


SURVEYING.  -39 

PROBLEM  VII.  To  find  the  Area  of  a  Square  or  Para?- 
lefagram. 

RULE.  Multiply  the  length  into  the  breadth  ;  the  Product 
will  be  the  Area. 

PROBLEM  VIII.  To  find  the  Area  of  a  Rhombus  or 
Khomboides. 

RUXE.  Drop  a  Perpendicular  from  one  of  the  Angles  to  its 
opposite  Side,  and  multiply  that  Side  into  the  Perpendicular  ; 
the  Product  will  be  the  Area. 

PROBLEM  IX.     To  find  the  Area  of  a  Triangle. 

RULE  1.  Drop  a  Perpendicular  irom  one  of  the  Angles  to  its 
opposite  Side,  which  may  be  called  the  Base  ;  then  multiply 
the  Base  by  half  the  Perpendicular,  or  the  Perpendicular  by 
half  the  Base  ;  the  Product  will  be  the  Area.  Or,  multiply  the 
whole  Base  by  the  whole  Perpendicular,  and  half  the  Product 
will  be  the  Area. 

RULE  2.  If  it  be  a  Right  Angled  Triangle,  multiply  one  of 
the  Legs  into  half  the  other  ;  the  Product  will  be  the  Area, 
Or,  multiply  the  two  Legs  into  each  other,  and  half  the  Pro- 
duct will  be  the  Area. 

RULE  3.  When  the  three  Sides  of  a  Triangle  are  known,  the 
Area  may  be  found  Arithmetically,  as  follows  : 

Add  together  the  three  Sides  ;  irom  halt  their  Sum  subtract 
each  side,  noting  down  the  Remainders  ;  multiply  the  half  Sum 
by  one  of  those  Remainders,  and  that  Product  by  another  Re- 
mainder, and  that  Product  by  the  other  Remainder  ;  the  Square 
Root  of  the  last  Product  will  be  the  Area. 

EXAMPLE.  Suppose  a  Triangle  whose  three  Sides  are  24r 
20,  and  18  Chains.  Demanded  the  Area. 

24  -f  20  -f  18=62,  the  Sum  of  the  three  Sides,  the  half  of 
which  is  31.  From  31  subtract  24,  20,  and  18  ;  the  three  Re- 
mainders will  be  7,  11,  and  13. 

31X7=217;  217X11=2387;  2387  X  13=3  1031,  the 
Square  Root  of  which  is  176.1,  or  17  Acres  2  Roods  and  17 


By  Logarithms. 

As  the  Addition  of  Logarithms  is  the  same  as  the  Multiple 
cation  of  their  corresponding  Numbers  ;  and  as  the  Number 
answering  to  the  one  half  of  a  Logarithm  will  be  the  Square 
Root  of  the  Number  corresponding  to  that  Logarithm  :  it  fol- 
lows, That  if  the  Logarithm  of  the  half  Sum  of  the  three  Sides 
and  the  Logarithms  of  the  three  Remainders  be  added  together/ 


40  SURVEYING. 

the  Number  corresponding  to  one  half  the  Sum  of  those 

arithms  will  be  the  Area  of  the  Triangle. 

The  half  Sum,  31          '&&-<         -  pSfi  1.49136 

The  first  Remainder,  7    -            -  -~  *  0.8451& 

The  second  Remainder,  11  •'  *'-'  1.04139 

The  third  Remainder,  13            ;v>  -  1.11394 


The  Square  of  the  Area,  31000 "  -  -  4.49179 

Area  176  Square  Chains  2.24589 

RULE  4.  When  two  Sides  of  a  Triangle  and  their  contained 
Angle,  that  is,  the  Angle  made  by  those  Sides,  are  given,  the 
Area  may  be  found  as  follows  : 

Add  together  the  Logarithms  of  the  two  Sides  and  the  Lo- 
garithmic Sine  of  the  Angle ;  from  their  sum  subtract  the  Lo- 
garithm of  Radius,  the  Remainder  will  be  the  Logarithm  of 
double  the  Area. 

EXAMPLE.  Suppose  a  Triangle  one  of  whose  Sides  is  10.5 
Rods  and  another  85,  and  the  Angle  contained  between  them 
28°  5X.  Demanded  the  Area. 

One  Side,  105  -  -  -         t   ?/         2.02119 

The  other  Side,  85  -  :  »  1.92942 

Sine  Angle,  280  5'    .  .  9.67280 

13.62341 
Subtract  Radius        ....  10.0000D 


Double  Area,  4200  Rods       •>  3.62341 

Answer.  2100  Rods. 

JVete.  Radius  may  be  subtracted  by  cancelling  the  Left-band  figure  of  .the 
Index,  or  subtracting  10,  without  the  trouble  of  setting  down  the  Cii 
phers. 

By  Natural  Sines. 

Multiply  the  two  given  Sides  into  each  other,  and  that  Pro- 
duct by  the  Natural  Sine  of  the  given  Angle  ;  the  last  Product 
will  be  double  the  Area  of  the  Triangle. 

Nat.  Sine  of  the  Angle  28O  5'  0.47076 

105  X  85=8925,  and  8925X0.47076=4201  tljje  double  Area 
of  the  Triangle. 

PROBLEM  X.  To  find  the  Jfreaof  a  Trapezoid. 


SURVEYING.  41 

RULE.  Multiply  half  the  Sum  of  the  two  parallel  Sides  by 
the  perpendicular  distance  between  them,  or  the  sum  of  the 
two  parallel  Sides  by  half  the  perpendicular  distance,  the  pro- 
duct will  be  the  Area. 

PROBLEM  XI.  To  find  the  Area  of  a  Trapezium,  or  trre- 
gular  Four  Sided  Figure. 

RULE.  Draw  a  Diagonal  between  two  opposite  Angles,  which 
will  divide  the  Trapezium  into  two  Triangles.  Find  the  Area 
of  each  Triangle  and  add  them  together.  Or,  multiply  the 
Diagonal  by  half  the  Sum  of  the  two  perpendiculars  let  fall 
upon  it,  or  the  Sum  of  the  two  perpendiculars  by  half  the  Dia- 
gonal, the  product  will  be  the  Area. 

Note.  Where  the  length  of  the  four  Sides  and  of  Uje  Diagonal  is  known, 
the  Area  of  the  two  Triangles,  into  which  the  Trapezium  is  divided,, 
may  be  calculated  Arithmetically,  according  to  PROS.  IX.  Rule  3. 

PROBLEM  XII.  To  find  the  Area  of  a  Figure  containing 
more  than  Four  Sides. 

RULE.  Divide  the  Figure  into  Triangles,  and  Trapezia,  by 
drawing  as  many  Diagonals  as  are  necessary,  which  Diagonals 
must  be  so  drawn  as  not  to  intersect  each  other  ;  then  find  the 
Area  of  each  of  the  several  Triangles  or  Trapezia,  and  add 
them  together ;  the  sum  will  be  the  Area  of  the  whole  Figure. 

»Vote.  A  little  practice  will  suggest  the  most  convenient  v/ay  of  drawing 
the  Diagonals ;  but  whichever  way  they  are  drawn,  provided  they  do 
not  intersect  each  other,  the  whole  Area  will  be  found  the  same. 

PROBLEM  XIII.      Respecting  Circles. 

RULE  1.  If  the  Diameter  be  given  the  Circumference  may 
be  found  by  one  of  the  following  proportions  :  as  7  is  to  22,  or 
more  exactly,  as  113  is  to  355,  or  in  Decimals,  as  1  is  to  3. 14159, 
so  is  the  Diameter  to  the  Circumference. 

RULE  2.  If  the  Circumference  be  given  the  Diameter  may 
be  found  by  one  of  the  following  proportions  :  as  22  is  to  7,  or 
as  355  is  to  113,  or  as  1  is  to  0.31831,  so  is  the  Circumference 
to  the  Diameter. 

RULE  3.  The  Diameter  and  Circumference  being  known, 
multiply  half  the  one  into  half  the  other,  and  the  product  will 
be  the  Area. 

RULE  4.  From  the  Diameter  only,  to  find  the  Area :  multi- 
ply the  Square  of  the  Diameter  by  0.7854,  and  the  product  will 
lie  the  Area. 

RULE  5.  From  the  Circumference  only  to  find  the  Area : 

K 


12  SURVEYING, 

multiply  the  Square  of  the  Circumference  by  0.07958,  and  the 
product  will  be  the  Area. 

RULE  6.  The  Area  being  given  to  find  the  Diameter  :  divide 
the  Area  by  0.7854,  and  the  Quotient  will  be  the  Square  of  the 
Diameter ;  from  this  extract  the  Square  Root,  and  you  will 
have  the  Diameter. 

RULE  7.  The  Area  being  given  to  find  the  Circumference  : 
divide  the  Area  by  0.07958,  and  the  quotient  will  be  the  Square 
of  the  Circumference  ;  from  this  extract  the  Square  Root,  and 
vou  will  have  the  Circumference. 


SECTION  II. 

The  following  CASES  teach  the  most  usual  methods  of  taking 
the  Survey  of  Fields ;  also,  how  to  protract  or  draw  a  Plot  ot 
them,  and  to  calculate  their  Area. 

Note.  The  FIELD  BOOK  is  a  Register  containing  the  length  of  the  Sides 
of  a  Field,  as  found  by  measuring  them  with  a  Chain  ;  also  the  Bear- 
ings or  Courses  of  the  Sides,  or  the  Quantity  of  the  several  Angles,  a? 
found  by  a  Compass  or  other  instrument  for  that  purpose ;  together  with 
such  Remarks  as  the  Surveyor  thinks  proper  to  make  in  the  Field. 


CASE  I. 

To  survey  a  Triangular  Field. 

Measure  the  Sides  of  the  Field  with  a  Chain,  and  enter  theii 
several  lengths  in  a  FIELD  BOOK,  protract  the  Field  on  Paper, 
and  then  find  the  Area  by  PROB.  IX.  Rule  1 .  Or,  without  plot- 
ting the  Field,  calculate  the  Area  by  PROB.  IX.  Rule  3. 

Fig.  46. 
FIEiLDBOOK.     See  Fig.  46. 

Chains. 

AB  20 

BC  -  .     -         24 

CA  18 

To  find  the  Area. 

Ch.  L. 

Base  BC    -        -        24.00 
HalfPerp.AD   -          7.34 

9600 


SURVEYING. 

9600 
7200 
16800 


Acres  17)61600 
4 

Roods  2)  46400 
40 


Rods  18)  56000 

Acres    Roods        Rods 
Area  17  —  2  —  18.56 

Note.  When  there  are  ciphers  at  the  Right  Hand  of  the  Links,  they 
may  be  rejected  ;  remembering  to  cut  off  a  proper  number  of  figured 
according  to  Decimal  Rules. 

Observe,  That  in  measuring  with  a  Chain,  slant  or  inclined 
Surfaces,  as  the  Sides  of  Hills,  should  be  measured  horizontally, 
and  not  on  the  Plane  or  Surface  of  the  Hill ;  otherwise,  a  sur- 
vey cannot  be  accurately  taken.  To  effect  this,  the  lower  end 
of  the  Chain  must  be  raised  from  the  ground,  so  as  to  have  the 
whole  in  a  horizontal  Line  ;  and  the  end  thus  raised  must  be 
directly  over  the  Point  where  the  Chain  begins  or  ends,  accord- 
ing as  you  are  ascending  or  descending  a  Hill ;  which  Point  may 
be  ascertained  by  a  Plummet  and  Line. 


CASE  II. 

To  survey  a  Field  in  the  form  of  a  Trapezium. 

Measure  the  several  sides,  and  a  Diagonal  between  two  op- 
posite Angles  ;  protract  the  Field,  and  find  the  Area  by  PROB- 
LEM XI.  Or,  without  protracting  the  Field,  calculate  the  Area 
according  to  the  JVbte  at  the  end  of  that  PROBLEM. 

Fig.  51. 
FIELD  BOOK.     See  Fig.  51. 

Ch.  L. 
AB 
BC 
CD 

DA       . 
Diagonal  AC 


27.50 
11.70 
21.50 
14.70 
28. 


44 


SURVEYING. 


To  protract  this  Trapezium. 

Draw  the  Side  AB  the  given  length  ;  with  the  Diagonal  AC 
28  and  the  Side  BC  11.70  describe  cross  Arches  as  at  C,  from 
A  and  B  as  Centres  ;  and  the  point  of  intersection  will  represent 
that  corner  of  the  Field  :  then,  with  the  Side  CD  21.50  and  the 
Side  AD  14.70,  describe  cross  Arches  as  at  D,  from  A  and  C  as 
Centres ;  and  the  point  of  intersection  will  represent  that  cor- 
ner of  the  field. 


To  find  the  Area. 


Perpendicular  B  a 
—  Dm 


Half  Diagonal  AC 


11.34 
11.10 

22.44 

14.00 

897600 
2244 

Acres  31)41 6 
4 

Rood  1)664 
40 


Rods  26)560 
Acres    Rood        Hods 
Area  31  —  1  —  26.56 

Note.  The  Perpendiculars  need'  not  be  actually  drawn  ;  their  length  may 
be  obtained  as  follows :  From  the  Angle  opposite  the  Diagonal  open  the 
Dividers  so  as  when  one  Foot  is  in  the  angular  Point,  as  at  B,  the  other, 
being  mored  backwards  and  forwards,  may  just  touch  the  Diagonal  at  a, 
and  neither  go  the  least  above  or  below  it ;  that  distance  in  the  Dividers 
being  measured  on  the  Scale  will  give  the  length  of  the  Perpendicular* 


CASE  III. 

To  survey  a  Field  which  has  more  than  four  Sides,  by  the  Chain 

easure  the  several  Sides,  and  from  some  one  of  the  Angles? 
which  the  others  may  be  seen,  measure  Diagonals  to 


SURVEYING,  4L 

them  ;  draw  a  Plot  of  the  Field,  and  find  the  Area  by  PROB- 
LEM XII. 


FIELD  BOOK.  See  Fig.  52. 


Fig.  52. 


AB 
BC 
CD 
DE 
EF 
FA 


Ch.  L. 
30.60 
20.40 
22.40 
16.20 
13.50 
28. 


Diagonals. 


AC 
AC 
AE 


Ch.  JL. 
45. 
35. 
24.20 


To  protract  this  Field. 

Draw  the  side  AB,  making  it  the  given  length  30.60;  with 
the  Diagonal  AC  45  and  the  Side  BC  20.40,  describe  cross 
Arches  as  at  C,  from  the  Points  A  and  B  as  Centres,  and  the 
Point  of  intersection  will  represent  that  Corner  of  the  Field  : 
draw  the  Side  BC  and  the  dotted  Diagonal  AC  ;  with  the  Dia- 
gonal AD  35  and  the  Side  CD  22.40,  describe  cross  Arches  as 
at  D,  from  the  Points  A  and  C,  and  draw  the  Side  CD  and  the 
dotted  Diagonal  AD.  Proceed  in  this  manner  till  all  the  Sides 
and  Diagonals  are  drawn. 


To  find  the  Area* 

The  Field,  being  plotted,  may  be- divided  into  one  Trapezium 
and  two  Triangles  ;  the  Area  of  which  is  calculated  as  fol- 
lows : — 

L 


SURVEYING. 


The  Trapezium  ABCD. 


Perpend.  B  a 
—      Do 


Half  Diag.  AC 


Square  Chains 


11.68 
17.10 


143900 
5756 
5756 

647.5500 


The  Triangle  AFE. 
Perpend.  En  -        -        11.65 

Half  Side  AF  -        -  14 


Square  Chains 

Acres  Roods    Rods 
Jrca  98  —  0  —  34.4 


4660 
1165 

163.10 


The  Triangle  ADE. 
HalfPerp.Em 
Diag.  AD         i'->;.-- 


Square  Chains 


4.30 
35 

2450 
1470 

171.50 


Trap.  ABCD 
Triangle  ADE 
Triangle  AFE 


647.6;V 
171.50 
163,10 

Acres  98)215 
4 

Roods   .860 

40 

Rods  34)400 


REMARKS. 

As  each  of  the  Sides  of  the  several  Triangles,  into  which  the 
preceding  Plot  of  a  Field  is  divided,  is  known  from  the  Field 
Book,  the  Area  of  the  Field  may  be  calculated  Arithmetically,  by 
finding  the  Area  of  each  Triangle,  according  to  PROB.  IX.  Rule 
3  ;  and  then  adding  the  whole  together.  This  method,  though 
it  may  require  more  time,  is  preferable  to  the  other,  because 
more  accurate.  Indeed  it  is  always  better  to  calculate  the  Area 
of  a  Field  Arithmetically  than  Geometrically ;  for  in  the  former 
no  two  persons  can  differ  in  their  calculations ;  whereas,  ac- 
cording to  the  latter,  which  is  the  common  method  of  casting 
the  contents  of  a  Field,  it  is  hardly  to  be  expected  that  any  two 
persons  will  perfectly  agree.  The  inaccuracy  of  Scales,  and 
the  difficulty  of  determining  with  precision  the  length  of  Sides 
and  Perpendiculars  with  a  Scale  and  Dividers,  render  it  almost 
if  not  quite  impossible  to  obtain  the  exact  Area  of  a  Field,  in 
the  method  commonly  practised,  even  if  the  Surveyor  has  mea- 
sured it  accurately  in  the  first  place. 

Other  methods  of  taking  the  Survey  of  a  Field  by  the  Chain 
only  are  mentioned  in  some  Treatises  on  this  subject,  but  they 


SURVEYING.  4*7 

are  rather  curious  than  useful ;  and  it  is  much  better  to  ascer- 
tain the  Angles  by  an  accurate  Compass,  or  some  instrument 
designed  purposely  for  taking  Angles. 


CASE  IV. 

To  Survey  a  Field  with  a  Chain  and  Compass. 

Measure  the  length  of  the  Sides  with  a  Chain,  and  take  their 
bearing  or  Course  with  a  Compass  ;*  enter  these  in  a  Field 
Book ;  plot  the  Field  on  paper,  and  calculate  the  Area  by  the 
directions  already  given. 

To  protract  or  draw  a  Map  of  a  Field.. 

Draw  a  Line  to  represent  a  Meridian,  or  North  and  South 
Line,  from  which  lay  off  a  Bearing  or  Course  of  the  first  Side 
of  the  Field,  with  a  Protractor  or  irom  a  Line  of  Chords  ;  and 
from  a  Scale  of  equal  parts,  measure  the  length  of  the  Side  and 
draw  a  Line  to  represent  it. 

At  the  end  of  this  Line  draw  a  Line  parallel  to  the  Meridian 
Line,  and  then  lay  off  the  second  Side  of  the  Field  as  before 
taught ;  proceed  in  the  same  manner  to  draw  parallel  Lines, 
and  lay  off  the  several  Sides  till  the  whole  is  protracted. 

In  protracting  a  Field,  let  the  top  of  the  paper  be  considered 
as  North,  the  bottom  South,  the  right  hand  East,  and  the  left 
hand  West ;  lay  the  Course  to  the  right  or  left  of  the  Meridian 
Line,  according  as  it  is  East  or  West,  and  from  the  upper  or 
lowe?  part  of  the  Line,  according  as  it  is  North  or  South. 

In  all  protractions,  if  the  end  of  the  last  distance  falls  exactly 
on  the  point  from  which  you  began,  the  Course  also  being  right, 
the  Field  work  and  protraction  are  truly  taken  and  performed  ; 
if  not,  an  error  must  have  been  committed  in  one  of  them :  in 
such  cases,  make  a  second  protraction  ;  if  this  agrees  with  the. 
former,  it  is  to  be  presumed  the  fault  is  in  the  Field  work ;  a 
re-survey  must  then  be  taken. 

*  A  Compass  may  be  so  constructed  with  two  Indexes,  one  moveable  and 
lUe  other  fixed,  as  to  ascertain  the  Angle  made  by  two  Sides,  without  refer- 
ence to  the  Bearing  of  those  Sides.  Such  a  Compass  would  be  particularly 
useful  in  surveying  Land  where  there  are  mineral  substances  which  have  an 
influence  upon  the  Compass  Needle,  attracting  it  one  way  or  the  other,  ami 
thus  rendering  it  impossible  to  take  a  Course  by  it  with  precision. 


4S 


SURVEYING, 


, 

EXAMPLE  I. 


FIELD  BOOK.     See  Fig.  53.  , 

Ch.  L.    r 

AB.  N.  70  Q'  W.  28.20   ?B! 
BC.  N.  74  0  E.   39.50 
CD.  S.   9  0   E.   38. 
DE.  3N".  63  20   W.  14.55 
EA.  S.  74  0  W.  28.60 

Acres    Rood  Rods 
Area     117—1—6 


REMARKS. 


The  Sides  of  the  several  Triangles  into  which  the  Plot  of  a 
Field  is  divided  may  be  found  by  Trigonometry ;  and  then  the 
Area  of  each  Triangle  may  be  calculated  according  to  PROB. 
IX.  Rule  3.  The  Sum  of  the  Areas  of  the  several  Triangles 
will  be  the  Area  of  the  whole  Field.  This  method  may  require 
more  time,  but  it  is  perfectly  accurate,  since  no  dependence  is 
placed  on  the  uncertain  measurement  of  Scale  and  Dividers. 

In  the  preceding  EXAMPLE,  suppose  the  Field  divided  into 
three  Triangles.  See  Fig.  53.  In  the  Triangle  EAB,  the  Sides 
EA  and  AB  are  known  from  the  FIELD  BOOK,  and  their  contained 
Angle  is  known  from  the  Bearing  of  the  Sides.  The  other 
Angles  and  the  Side  EB  may  be  found  by  OBLIQUE  TRIGONOME- 
TRY, CASE  IIL  ;  and  then  there  will  be  the  three  Sides  to  find 
the  Area.  In  the  Triangle  EBC,,  the  Side  BC  is  known  from 
the  FIELD  BOOK,  and  the^Sjde  EB  is  found  as  above  mentioned  ; 
the  Angle  EBA  is  also  found  as  above  ;  this  subtracted  from 
the  Angle  ABC,  which  may  be  found  from  the  bearing  of  the 
Sides  AB  and  BC,  will  leave  the  Angle  EBC  :  there  will  then 
be  the  two  Sides  and  their  contained  Angle  to  find  the  third 
Side ;  and  this  being  found,  there  will  be  the  three  Sides  to  find 
the  Area.  In  the  Triangle  EDC,  the  Sides  DE  and  DC  are 
known  from  the  FIELD  BOOK,  and  their  contained  Angle  is 
known  from  the  bearing  of  the  Sides.  The  Side  EG  and  the 
Area  may  be  found  as  above. 

It  is  recommended  to  the  Learner  to  make  these  calculsu 


SURVEYING. 


49 


tions,  as  it  will  improve  him  in  the  knowledge  of  Trigonome- 
try. 

Note.    Two  Sides  and  their  contained  Angle  being  given,  the  Area  may 
be  found  by  PROB.  IX.  Rule  4. 

Another  Method  of  protracting  Fields. 

Without  drawing  parallel  Lines  at  the  end  of  each  Side>  a 
Field  may  be  protracted  by  the  Angles  made  by  the  several 
Sides ;  and  the  Angle  made  between  any  two  Sides  may  be 
found  by  the  following  RULES. 

RULE  1.  If  the  course  or  bearing  of  one  «f  the  Sides  is 
northerly  and  the  other  southerly,  one  easterly  and  the  other 
westerly,  subtract  the  less  Course  from  the  greater,  the  remain- 
der will  be  the  Angle  between  them. 

RULE  2.  If  one  is  northerly  and  the  other  southerly,  and 
both  easterly  or  westerly,  add  both  Courses  together  ;  the  sum 
will  be  the  Angle  between  them. 

RULE  3.  If  both  are  northerly  or  southerly,  and  one  easter- 
ly and  the  other  westerly,  subtract  the  sum  of  both  from  180° ; 
the  remainder  will  be  the  Angle  between  them. 

RULE  4.  If  both  are  northerly  or  southerly,  and  both  east- 
erly or  westerly,  add  90°,  the  less  Course,  and  the  Comple- 
ment of  the  greater  together  ;  the  sum  will  be  the  Angle  be- 
tween them. 

To  protract  a  Field  according  to  the  preceding  Rules  is  pre- 
ferable to  the  method  of  doing  it  by  parallel  Lines,  though  it 
may  not  be  so  easy  to  the  Learner  at  first.  It  is  difficult  to 
draw  parallel  Lines  with  perfect  accuracy,  particularly  without 
a  parallel  Rule  ;  and  a  small  deviation  from  a  true  Line  may 
make  considerable  difference  in  the  Plot  of  a  Field. 


EXAMPLE  II. 
FIELD  BOOK.     -See  Fig.  58. 

Ch.  L. 

AB.  N.  160  30'  E.  22. 
BC.  N.  82   0   E.  19.60 
CD.  S.  17   0   E.  24. 
DE.  S.  37   0  W.  22. 
EA.  N.  49   0  W.  25.20 


Area  85  Acres. 


M 


50 


SURVEYING. 


To  draw  a  Plot  of  this  Field,  according  to  the  preceding 
RULES. 

Having  drawn  the  Side  AB,  according  to  the  directions  he- 
fore  given  for  laying  off  the  first  Course  and  Distance,  com* 
pare  the  first  and  second  Courses  together,  and  they  will  be 
found  to  he  both  northerly  and  both  easterly  ;  consequently, 
the  Angle  between  them  is  found  by  RULE  4,  as  follows  :  90° 
added  to  16°  30X  the  less  Course,  and  8°  the  Complement  of 
the  greater,  the  sum  is  114°  30',  for  the  Angle  at  B.  Compare 
the  second  and  third  Courses,  and  they  will  be  found  to  be  one 
northerly  and  one  southerly,  and  both  easterly  ;  consequently, 
according  to  RtiLE  2,  82°  the  second  Course  added  to  17°  the 
third  Course,  the  sum  99°  is  the  Angle  at  C.  The  third  and 
fourth  Courses  are  both  southerly,  and  one  easterly  and  the 
other  westerly.  -The  Angle  between  them  at  D  is  126°  ;  for 
17°  the  third  Course  added  to  37°  the  fourth  Course  is  54°, 
which  subtracted  from  180°  leaves  126°,  according  to  RULE  3. 
The  fourth  and  fifth  Courses  are  one  southerly  and  the  other 
northerly,  and  both  westerly.  According  to  RULE  2,  37°  the 
fourth  Course  added  to  49°  the  fifth  Course,  the  sum  86°  is  the 
Angle  at  E. 

A  little  practice  will  render  this  mode  of  protracting  a  Field 
familiar  and  easy,  and  an  attention  to  the  Courses  will  show  in. 
what  direction  the  Angle  is  to  be  made. 


EXAMPLE  III. 
FIELD  BOOK.     See  Fig.  66. 


Fig.  66 


I> 


SURVEYING. 


51 


Ch.  L. 

AB. 

N. 

560 

15' 

E. 

21.60 

BC. 

N. 

26 

30 

E. 

13.44 

CD. 

S. 

71 

30 

E. 

18.96 

DE. 

S. 

26 

30 

E. 

13.44 

EF. 

S. 

71 

30 

W. 

18.96 

FG. 

S. 

45 

0 

E. 

8.47 

GH. 

S. 

63 

30 

E. 

13.44 

HL 

N. 

45 

0 

E. 

8.47 

IK. 

S. 

26 

30 

E. 

13.44 

KL. 

S. 

45 

0 

W. 

8.47 

LM. 

S. 

63 

30 

W. 

13.44 

MN. 

N» 

76 

0 

W. 

24.73 

NA. 

N. 

36 

45 

W, 

30. 

Acres    Rood 

Rods 

Area, 

167  — 

1  —  30 

The  above  Field  may  be  protracted,  and  its  Area  calculated 
according  to  the  directions  given  in  the  preceding  EXAMPLES. 


Several  Field  Books  to  exercise  the  Learner  in  plotting  Fields  and 
calculating  their  Area. 

Ch.JL 


No.  I 

„ 

Rods. 

8. 

N. 

53015' 

W.      11.60 

1. 

N.     150  o' 

E. 

320 

9. 

N. 

36  45 

E.     19.20 

2. 

N.     37  30 

E. 

160 

10. 

N. 

22  30 

E.      14. 

3. 

East 

120 

11. 

S. 

76  45 

E 

.     12. 

4. 

S.      11     0 

E. 

200 

12. 

S. 

15     0 

W 

.      10.85 

5. 

South 

216 

13. 

S. 

16  45 

W 

.     10.12 

6. 

West 

160 

Acres  Roods 

Rods. 

7. 

S.      36  30 

W. 

160 

Area  110  —  2  —  23 

8. 

N.     38  15 

W. 

136 

___ 

Acres  Roods  Rods 

No.  III. 

Rods. 

Area  744  — 

3  — 

28 

1. 

S. 

65040' 

W. 

49.7 

2. 

S. 

67  15 

W. 

34.5 

No.  II. 

Ch.L. 

3. 

S. 

54     0 

W. 

17.0- 

1. 

N.     750  Ox 

E. 

13.70 

4. 

-S. 

20     0 

W. 

•5.8 

2. 

N.     20  30 

E. 

10.30 

5. 

S. 

7  30 

E. 

29.4 

3, 

East 

16.20 

6. 

N. 

83     0 

E. 

107.4 

4. 

S.      33  30 

W. 

35.30 

7. 

N. 

5  50 

W. 

22. 

5. 

S.      76     0 

W. 

16. 

8. 

N. 

18  30 

W, 

46, 

6. 

North 

9. 

Acres  Roo^Rods, 

7. 

S.      84    0 

W. 

11.60 

Area  34  —  1— 

19 

SURVEYING. 


No.  IV. 

Rods. 

Rods. 

1. 

N. 

430  (X 

W. 

12.44 

16. 

N. 

18°30/ 

W. 

39. 

2. 

N. 

64     0 

W. 

8. 

17. 

N. 

86     5 

E. 

26.7 

3, 

N. 

52     0 

w. 

14.60 

Acres  Rood  Rods 

4. 

N. 

37     5 

w. 

51.36 

Area  48  —  I 

—  12 

5. 

N. 

15  30 

w. 

21.76 



6. 

N. 

20  40 

w. 

44.60 

No.  VII. 

Ch.  L. 

7. 

N. 

88  20 

E.   167.60 

1. 

N. 

0045' 

W. 

9. 

8. 

S. 

34  40 

E. 

71.20 

2. 

N. 

19  30 

W. 

5.35 

9. 

S. 

75     0 

W. 

69.72 

3. 

N. 

23     0 

W. 

4.09 

10. 

S. 

55     0 

W. 

64.60 

4. 

N. 

41  35 

w. 

6.15 

11. 

S. 

25     0 

W. 

18.12 

5. 

N. 

3     0 

w. 

36.75 

Acres  Roods  Rods. 

6. 

S. 

86  50 

w. 

13.33 

Area 

97  —  2  —  29 

7. 

N. 

2  15 

w. 

17.65 

.. 

8. 

N. 

85  45 

E. 

12.56 

No.V. 

Rods. 

9. 

S. 

2  10 

E. 

8. 

1. 

S. 

11050' 

W. 

34.6 

10. 

N. 

86  45 

E. 

7.38 

2. 

S. 

63  20 

E. 

93.6 

11. 

S, 

3  15 

E. 

13.20 

3. 

N. 

4     0 

W. 

34.9 

12. 

N. 

87     0 

E. 

29.92 

4. 

S, 

89  55 

E. 

40.1 

13. 

.  N. 

49  20 

E. 

4.04 

5. 

N. 

5  20 

W. 

35.5 

14. 

North 

2.23 

6. 

N. 

69  40 

W. 

60. 

15, 

N. 

50  35 

E. 

6.50 

7. 

S. 

78     0 

W. 

30.6 

16. 

S. 

22  50 

E. 

17.94 

8. 

N. 

67  20 

W. 

1.2 

17. 

S. 

34     0 

W. 

3.50 

9. 

S. 

72  30 

w. 

10.4 

18. 

S. 

41     0 

W. 

3. 

10. 

S. 

66  55 

w. 

15.2 

19. 

S. 

22  50 

w. 

9.25 

Acres  Rood  Rods. 

20. 

S. 

3  40 

E. 

2.64 

Area  41  —  1  —  34 

21. 

S. 

86     0 

w. 

2.50 

_____ 

22. 

S. 

0  25 

w. 

14.50 

No.  VI 

Rods. 

23. 

S. 

2     0 

w. 

5.38 

1. 

S. 

340  o' 

E. 

42.8 

24. 

S. 

10     0 

E. 

11.75 

2; 

S. 

29     0 

E. 

69.4 

25. 

S. 

86     0 

W. 

34.60 

3. 

S. 

64  50 

W. 

53. 

Acres  Roods  Rods 

4. 

S. 

25     0 

E. 

4. 

Area  268  — 

3  — 

7 

5. 

S. 

66  30 

W. 

,39. 



6. 

N. 

25     0 

W. 

4. 

No.  VIII. 

Rods 

7. 

S. 

64  45 

W. 

32.2 

1. 

S. 

6030' 

E. 

19.1 

3, 

N. 

30  30 

w. 

18.3 

2. 

S.' 

63  30 

E. 

14.36 

9. 

N. 

56  30 

E. 

34.5 

3. 

S. 

67     0 

E. 

10.68 

10. 

N. 

64     0 

E. 

12.5    4; 

N. 

88     0 

E. 

13.3 

11. 

N. 

49     0 

E. 

14. 

5. 

S. 

31  30 

W. 

32.44 

12. 

26  10 

W. 

19.3 

6. 

S. 

31  55 

W. 

96.5 

13. 

N. 

21     0 

W. 

18.3 

7. 

S. 

33  25 

W. 

34,9 

14. 

N. 

44  10 

W. 

18. 

8. 

S. 

20  45 

E. 

3.68 

15, 

N. 

(4  40 

E, 

30.5 

9. 

S. 

16  15 

w. 

64. 

SURVEYING. 


10.  N.  52°30X  W.  12.8 

11.  S.  45     0  W.  18.24 

12.  S.  69     0  W.  21.4 

13.  S.  12  40  W.       9.4 

14.  S.  84  20  W.       9.5 

15.  X.  22  15  W.  24. 

16.  North  9.8 

17.  N.  29  15  W  30.6 

18.  N.  44  25  W  21.8 

19.  N.  61  30  W  23.1 

20.  N.  41     0  W  10.8 


21.  N.     360  o'    E.  41.56 

22.  S.    68       0     E.  80.6 

23.  N.  44     30     E.  20.4 

24.  N.     2     30     W.  41. 

25.  N.   14     45     W.  62.32 

26.  N.  16       0     W.  14.8 

27.  N.     1     45     W.  14.8 

28.  N.  82     30     W.  99. 

Acres  Rood  Rods 
Area  135  —  1  —  15 


CASE  V. 

To  survey  a  field  from  one  station,  at  any  place  within  the  Field, 
from  which  the  several  Angles  may  be  seen. 

Take  the  Bearing  of  the  Angles,  and  measure  their  Distance 
from  the  Station. 


FIELD  BOOK.     See  Fig.  61. 


Fig.  61. 


Ch.  L. 

N. 

200W. 

8.70 

N. 

60  E. 

10. 

N. 

87  E. 

11.40 

S. 

15  E. 

10.50 

S. 

60  W. 

12. 

N. 

65  W. 

8.78 

From  Station  to  A. 
B. 
C. 
D. 
E. 
F. 

To  protract  this  Field. 

Draw  a  Meridian  Line  as  N.  S.  From  some  point  in  that 
Line  as  a  Centre  lay  off  the  Bearing  and  Distance  to  the  several 
Angles,  and  draw  Lines  from  one  Angle  to  another,  as  AB,  BC, 
CD,  &c. 

N 


SURVEYING. 


To  find  the  Area. 

The  Area  may  be  calculated  according  to  PROB.  XII.  by 
measuring  Diagonals  and  Perpendiculars  ;  or  more  accurately 
according  to  PROB.  IX.  Rule  4. 

As  the  Bearing  and  Distance  of  the  Lines  from  the  Station 
to  the  several  Angles  are  known,  two  Sides  and  their  contained 
Angle  are  given  in  each  of  the  Triangles  into  which  the  Plot 
is  divided ;  the  Area  may,  therefore,  be  readily  calculated  by 
the  Rule  above  referred  to. 

Note.  As  in  the  operation,  the  Logarithm  of  Radius  is  to  be  subtracted 
from  the  Sum  of  the  other  Logarithms,  it  may  be  done  by  rejecting  the 
Left-hand  figure,  without  the  trouble  of  putting  down  the  Ciphers  and 
subtracting. 


Triangle  aAB. 
aA,  8.70       - 
aB,  10 
Sine  AaB,  80d      - 

JDoub.  Area,  85.7 

0.93952 
1.00000 
9.99335 

Triangle  aDE. 
aD,  10.50    -        - 
aE,  12 
Sine  DaE,  75°      - 

Doub.  Area,  122 

1.02119 
1.07918 
9.98494 

1.93287 

2.08531 

Triangle  aBC. 
aB,10 
aC,  11.40     - 
Sine  BaC,  27°       - 

1.00000 
1.05690 
9.65705 

Triangle  aEF. 
aE,  12 
aF,  8.78 
Sine  EaF,  55°       - 

1,07918 
0.94349 
9.91336 

Doub.  Area,  51.8 

1.71395 

Doub.  Area,  86.3 

1.93603 

Triangle  aCD. 
aC,  11.40    - 
aD,  10.50    - 
Sine  CaD,  78°     - 

Ooub.  Area,  117 

1.05690 
1.02119 
9.99040 

Triangle  aFA. 
aF,8.78       - 
aA,  8.70 
Sine  FaA,  45°      -        - 

Doub.  Area,  54    - 

0.94349 
0.93952 

9.84948 

2.06849 

1.73249 

Triangle  aAB 
aBC 
aCD 
aDE 
aEF 
aFA 

85.? 
51.8 
117. 
122. 
86.3 
54. 

Double  Area 

516.8 

Area 

25)84 

4 
5  3- 


Aeres 

25—3 


14 


—   14.4 


To 
v»«Mr 
Fro«  tke 
of  fee 


CASE  VI. 

KM  fnm  ~m*  •** 

e  take 
witk  a  C 


FIELD  BOOK,     Set  /%.  59. 


C&fe 

FG.     N".     TOO  W.     14JB) 

FA.  N.     50     W.     laift 

FB.  N.    as   w.    j*ao 
v.    10   w.    sum 

FT.  N.  -  E.  1&S5 
FE.  N.  30  E.  S.30 
!*•*«»  •Firf^*» 


at  F.     Fnm  the  Foot 


> 


A^l 

<^i:c 


:  kc 


SURVEYING. 


CASE  VII. 

To  survey  a  Field  from  two  Stations  within  the  Field,  provided 
the  several  Jingles  can  be  seen  from  each  Station. 

Find  the  Bearing  from  each  Station  to  the  respective  Angles ; 
and  also  the  Bearing  and  Distance  from  one  Station  to  the 
other. 

Fig.  62. 


FIELD  BOOK.    See  Fig.  62, 


First  Station. 
AC.     N.     380  so' 


AD.  S.      69 

AE.  S.      59 

AF.  N.     63 

AG.  N.     21 
AH.  North. 


0  E. 

0  W. 

0  W. 

0  W. 


Second  Station. 

BC.  S,  820  <)' 

BD.  S.  17  0 

BE.  S.  28  0 

BF.  S.  49  0 

BG.  N.  76  0 
BH.  N.  24  0 


Stationary  Line  AB.  N.  14O  E.  20  Chains. 

To  protract  this  Field. 

At  the  first  Station  A,  draw  a  Meridian  Line  and  lay  off  the 
Bearings  to  the  respective  Angles ;  draw  the  Stationary  Line 
AB,  according  to  the  Bearing  and  Distance  ;  at  B,  draw  a  Me- 
ridian Line  parallel  to  the  other,  and  lay  of  the  Bearings  to 
the  Angles,  as  taken  from  this  Station ;  from  each  Station  dra^v 
Lines  through  the  Degree  which  shows  the  Bearing  of  each 
Angle,  as  marked  by  the  Protractor  or  Line  of  Chords,  and  the 
Points  where  those  Lines  intersect  each  other  will  be  the  An- 
gles of  the  Field.  Connect  those  angular  Points  together  by 
Lines,  and  those  Lines  will  represent  the  several  Sides  of  the 
field. 


SURVEYING, 


CASE  VIII. 

To  Survey  an  inaccessible  Field. 

Fix  upon  two  Stations,  at  a  convenient  distance  from  the 
Field,  from  each  of  which  the  several  Angles  may  be  seen  ; 
from  each  Station  take  the  Bearing  of  the  Angles  ;  and  take 
the  Bearing  and  Distance  from  one  Station  to  the  other. 

Fig.  67. 


FIELD  BOOK.     See  Fig.  67. 


First  Station. 

AE.  N.  90  15/  E. 

AF.  N.  16  0  E. 

AG.  N.  14  30  E. 
AD.  N.  39  0  E. 
AH.  N.  40  0  E. 
AC.  N.  72  0  E. 


Second  Station. 
BE.     N.     500     0'    W. 


BF.  N.     29     15  W. 
BD.     N.     24       0  W. 

BG.  N.     21     30  W. 
BH.     N.       5       0  E. 
BC.     N.     20     30  E, 

Ch.  L. 
Stationary  Distance  AB,  S.  88Q  30'  E.  19.20. 


The  directions  given  in  the  last  CASE  for  plotting  the  Field, 
will  apply  in  this  CASE  also  ;  and  the  Area  in  this  and  the  pre- 
ceding CASE  may  be  calculated  in  the  manner  pointed  out  in 
CASE  IV.  by  dividing  the  Plot  into  Triangles  and  measuring 
Diagonals  and  Perpendiculars.  Or  the  Sides  may  be  found  by 
Trigonometry,  and  the  Area  calculated  Arithmetically,  as 
already  taught, 

O 


58 


SURVEYING, 


CASE  IX. 


To  survey  a  Field  where  the  boundary  Lines  are  very  irregular 
without  noticing  with  the  Compass  every  small  Bend, 


Fig.  68. 


Begin  near  one  corner  of  the 
Field,  as  at  A,  Fig.  68.  and 
measure  to  the  next  large  Cor- 
ner, as  B,  in  a  straight  Line  ; 
noticing  also  the  Bearing  of 
this  Line.  From  the  Line 
take  Offsets  to  the  several 
Bends,  at  Right  Angles  from 
the  Line ;  noticing  in  the 
FIELD  BOOK  at  what  part  of  KT: 
the  Line  they  are  taken,  as  at 
A  1,  H  2, 1  3,  B  4.  Proceed  j 
in  the  same  manner  round  the 
Field.  In  the  Figure  the  dot- 
ted Lines  represent  the  sta- 
tionary Lines,  and  the  black 
.Lines  the  Boundaries  of  the  Field. 


FIELD  BOOK. 


Bearing  and  Distance, 

Offsets 

Bearing  arid  Distance. 

Offsets 

Ch.  L. 
AB.  N.  85<>  0'  E.         1L20 
at  5.40 
8.26 
the  end 

Ch.  L. 
0.56 
1.40 
0.36 
0.36 

Ch.  L. 
EF.  S.  67Q  50'  W.         8.20 
at  1.  4 
2.96 

5.88 
the  end 

Ch.  L. 
0.40 
0.36 
0.33 
1. 
0.12 

BC.  N.  7°  20'  E,          7.96 
at  2.36 

4.28 
the  end 

0.20 
0.36 
0.96 
0.30 

FG.  S.  27°  40'  E.         7.06 
at  2. 
the  end 

1.20 
0.24 
0.16 

CD.  N.  62°  (XW.        4.68 
at  4.34 

0.30 

GA.  S.  25°  20'  W.       6.48 
1     at  3.80 
the  end 

0.80 
0.40 

DE.  N.  11°  10'  W.      4.20 

0.30 

SURVEYING,  59 


To  protract  this  Field. 

Draw  the  stationary  Lines  according  to  the  directions  in 
CASE  IT.  From  A  make  an  Offset  of  56  Links  to  I ;  measure 
from  A  to  H  540  Links  and  make  the  Offset  H  2,  140  Links  ; 
measure  from  A  to  I  826  Links  and  make  the  Offset  I  3,  36 
Links  :  at  B  make  the  Offset  B  4,  36  Links.  Proceed  in  the 
same  manner  round  the  Field,  and  connect  the  ends  of  the  Off- 
sets by  Lines,  which  will  represent  the  Boundaries  of  the 
Field. 


To  find  the  Area. 

Find  the  Area  within  the  Stationary  Lines  as  before  taught ; 
then  of  the  several  small  Trapezoids,  Parallelograms  and  Trian- 
gles made  by  the  stationary  Lines,  Offsets  and  boundary  Lines, 
and  add  the  whole  together  :  thus,  add  56  Links  the  Offset  A 
1  to  140  Links  the  Offset  H  2  and  multiply  their  sum  196  by 
half  540  the  length  of  the  line  AH,  and  the  Product  52920 
Square  Links  will  be  the  Area  of  the  Trapezoid  AH  21  :  again, 
add  140  the  Offset  H  2  to  36  the  Offset  I  3  and  multiply  theiv 
Sum  176  by  half  286  the  length  of  the  Line  HI,  and  the  pro- 
duct 25168  Square  Links  will  be  the  Area  of  the  Trapezoid 
HI  32.  Proceed  in  the  same  manner  to  calculate  the  Area  of 
all  the  Trapezoids,  Triangles,  &c. 


CASE  X. 

To  survey  a  Field  by  taking  Offsets  both  to  the  Right  and  Left  ; 
that  is,  within  and  without  the  Fietd,  as  occasion  shall  require,  in 
consequence  of  the  Stationary  Lines  crossing  the  boundary  Lines : 
also.,  by  Intersections.,  that  is,  taking  the  bearing  of  an  inaccessible 
Corner  from  two  Stations. 

The  directions  given  in  the  preceding  CASE,  together  with 
the  following  FIELD  BOOK,  will  show  the  Learner  how  to  sur- 
vey a  Field  like  the  following,  and  also  to  protract  it  when  sur- 
veyed. 


60 


SURVEYING. 


Fig.  6S. 


FIELD  BOOK.     See 
.  69. 


Offsets 
to  the 
Left. 

Bearing  and  Distance. 

Offsets 
to  the 
Right. 

Remarks. 

Ch.  L. 
1.12 
3.40 
1.25 

Ch.  L. 

AB.  N.  88°0'W.       22.12 
at    4.25 
7.40 
13. 

Ch.  L. 

A  Tower  bears  from 
A.  N.  48°  W. 

0.45 

BC.  N.  27°45'W.     21.12 
,  at  4.10 
10.25 
15. 

1.20 
1.15 

From  B  the  Tower 
bears  N.  38°  30'  E. 

C  1.  S.  82°  15'  E.         5.45 
1,  2.  N.  70     0  E.       13.25 
2  D.  N.  20     0  E.         3.36 

From    C    go    into    the 
Field  to  1,  on  account  of 
some    impediment    on    or 
near    the    boundary  Line. 
At  D,  you  get  into  another 
Corner  of  the  Field. 

DF.  S.  35°0'E.        15.15 

E,  an  inaccessible  Corner, 
bears  from  D.  S.  65°  30'  E. 

2.20 
2.32 

FA.  S.  15°  15'  E.       15.10 
at  1.20 
7.45 
12.25 

0.36 

E,  the  inaccessible  Corner, 
bears  from  F 
N.  4°  W. 

Note.  To  draw  a  Tree,  House,  Tower,  or  any  other  remarkable  object, 
in  its  proper  place,  in  the  Plot  of  a  Field — From  any  two  stations,  whil* 
surveying  the  Field,  take  the  bearing  of  the  object ,  and  the  intersec- 
tion of  the  Lines,  which  represent  the  bearings,  will  determine  the 
place  of  the  object,  in  the  same  manner  that  the  Tower  is  drawn  in  the 
figure. 


SURVEYING.  61 


To  find  the  Area  of  the  above  Field. 

Find  the  Area  within  the  stationary  Lines,  and  then  of  the 
several  small  Trapezoids,  &c.  remembering  to  distinguish 
those  without  the  stationary  Lines  from  those  which  are  within. 
Subtract  the  Area  of  those  within  the  stationary  Lines  from 
the  Area  of  those  without,  and  add  the  Remainder  to  the  Area 
contained  within  the  stationary  Lines  ;  the  sum  will  be  the 
whole  Area  of  the  Field. 


SECTION  III. 

RECTANGULAR  SURVEYING,  or  an  accurate  method  of  calculating 
the  Jlrea  of  a  Field  Arithmetically,  from  the  FIELD  BOOK,  without 
the  necessity  of  protracting  it  and  measuring  with  a  Scale  and  Di- 
viders, as  is  commonly  practised. 

I.  Survey  the  Field  in  the  usual  method  with  an  accurate 
Compass  and  Chain,  and  from  the  FIELD  BOOK  set  down,  in  a 
Traverse  Table,  the  Course  or  Bearing  of  the  several  Sides, 
and  their  length  in  Chains  and  Links,  or  Rods  and  Decimal 
parts  of  a  Rod;  as  in  the  2d  and  3d  Columns  of  the  following. 


SURVEYING. 


00 


lot     en I     rt>»         I     CO         I     tO         I'  M 


n 


w       !   •*       I   £       I    w       I 

4*.          i     O          i     O  •     i£.  i 


J?0> • 


en  cn    I    o  *      |    co  w 
os  »»*    i    &  O   i    Co  v 


OD  O3 
4^  j** 
<»  00 

to  rfk. 


to  to 

b  b 
to,o-i 


-i  -a       eo 

CT«  eo   i    en  o 


n 


19143.9019  Sum  of  South  Areas 
4245.4016  North'  Do, 


2)14898.5003  Double  Area  of  the  Field; 


Acres  744)92501 
4 

Roods  3)70004 
40 

Rods  28)00160 

Acres    Roods    Rods 
Jreo  744  —  3  —  28 


SURVEYING.  63 

2.  Calculate  by  RIGHT  ANGLED  TRIGONOMETRY,  CASE  1,  or 
find  by  the  Table  of  Difference  of  Latitude  and  Departure,* 
ar  by  the  Table  of  Natural  Sines,|  the  northing  or  southing, 
easting  or  westing,  made  on  each  Course,  and  set  them  down 
against  their  several  Courses,  in  their  proper  Columns,  marked 
N.  S.  E.  W. 

vVo/e.  To  determine  whether  the  Latitude  and  Departure  for  any  parti* 
cular  Course  and  Distance  are  accurately  calculated,  square  each  of 
them  ;  and  if  they  are  right,  the  Sum  of  their  Squares  will  equal  the 
Square  of  the  distance,  for  the  following  reason  :  the  Latitude  and  De- 
parture represent  the  two  Legs  of  a  Right  Angled  Triangle,  and  the 
Distance  the  Hypothenuse  j  and  it  is  a  Mathematical  truth,  that  the 
Square  of  the  Hypothenuse  of  any  Right  Angled  Triangle  is  equal  to. 
the  Sum  of  the  Squares  of  the  two  Legs. 

3.  If  the  Survey  has  been  accurately  taken,  the  sum  of  the 
northings  will  equal  the  southings,  and  the  eastings  will  .equal 
the  westings.     If,  upon  adding  up  the  respective  Columns,  these 
are  found  to  differ  very  considerably,  the  Field  should  be  again 
surveyed  ;  as  some  error  must  have  been  committed,  either  in 
taking  the  Courses  or  measuring  the  Sides.     It  the  difference 
is  small,  a  judicious,  experienced  Surveyor  will  judge  from  the 
nature  of  the  ground  or  shape  of  the  Field  surveyed,  where 
the  mistake  was  most  probably  made,  and  will  correct  accord- 
ingly.    Or,  the  northings  and  southings  and  the  eastings  and 
westings  may  be  equalled  by  balancing  them,  as  follows  ;  sub* 
tract  one  half  the  difference  from  that  Column  which  is  the 
largest,  and  add  the  other  half  to  that  Column  which  is  the 
smallest ;  and  let  the  difference,  to  be  added  or  subtracted,  be 
divided  among  the  several  Courses,  according  to  their  length. 

In  EXAMPLE  I.  the  upper  numbers  are  the  northings,  &c.  as 
found  by  a  Table  of  Difference  of  Latitude  and  Departure. 
The  several  Columns  being  added,  the  northings  are  found  to 
exceed  the  southings  47  Links,  and  the  westings  to  exceed  the 
eastings  24  Links.  They  may  be  balanced  by  taking  24  Links 
from  the  northings,  and  adding  23  Links  to  the  southings ;  and 
taking  12  Links  from  the  westings,  and  adding  12  Links  to  the 
eastings.  Take  from  the  first  Course  of  the  northings  12  Links, 
from  the  second  7,  and  from  the  third  5 ;  to  the  first  southing 
add  7  Links,  to  the  second  10,  and  to  the  third  6  :  add  to  the 
first  easting  3  Links,  to  the  second  3,  to  the  third  4,  and  to  the 

*  For  an  explanation  of  this  Tahle,  and  the  manner  of  using  it,  see  the 
remarks  preceding  the  Table. 
t  >Stfe  the  Remarks  preceding  the  Table  of  Natural  Sin^s. 


64  SURVEYING. 

fourth  2  ;  take  from  the  first  westing  5  Links,  from  the  second 
4,  and  from  the  third  3.  The  lower  numbers  will  then  repre- 
sent the  northings,  &c.  as  balanced. 

4.  These  Columns  being  balanced,  proceed  to  form  a  De- 
parture Column,  or  a  Column  of  Meridian  Distances  ;  which 
shows  how  far  the  end  of  each  Side  of  the  Field  is  east  or  west 
of  the  station  where  the  calculation  begins.     This  Column  is 
formed  by  a  continual  addition  of  the  eastings  and  subtraction 
of  the  westings ;  or  by  adding  the  westings  and  subtracting  the 
eastings  :  See  EXAMPLE  I. 

The  first  easting  20.74  is  set  for  the  first  number  in  the  De- 
parture Column  ;  to  this  add  24.38  the  second  easting,  and  it 
makes  45.12,  for  the  second  number;  to  this  add  30.04  the 
third  easting,  and  it  makes  75.16,  for  the  third  number ;  to  this 
add  9.56  the  fourth  easting,  and  it  makes  84.72,  for  the  fourth 
number  ;  the  fifth  Course  being  south,  it  is  evident  the  Meri- 
dian Distance  will  remain  the  same,  therefore,  place  against  it 
the  same  easting  as  for  the  preceding  Course ;  from  this  sub- 
tract 39.95,  the  first  westing,  and  it  leaves  44.77,  for  the  sixth 
Course ;  from  this  subtract  23.75,  the  second  westing,  and  it 
leaves  21.02,  for  the  seventh  Course  ;  from  this  subtract  21.02 
the  last  westing,  and  it  leaves  0.0.  to  be  set  against  the  last 
Course,  which  shows  that  the  additions  and  subtractions  have 
been  accurately  made.  For  as  the  eastings  and  westings  equal 
each  other,  it  is  evident  that  one  being  added  and  the  other 
subtracted,  there  will  in  the  end  be  no  remainder. 

5.  The  next  step  hi  the  process  is  to  form  a  second  Depar- 
ture Column,  the  numbers  in  which  show  the  Sum  of  the  Me- 
ridian Distances  at  the  end  of  the  first  and  second,  second  and 
third,  third  and  fourth  Courses,  &c. 

The  first  number  in  this  column  will  be  the  first  in  the  other 
Departure  Column  ;  to  which  add  the  second  number  in  that 
Column  for  the  second  in  this :  for  the  third  add  the  second  and 
third ;  and  for  the  fourth,  the  third  and  fourth ;  and  so  on  till 
the  Column  be  completed.  See  EXAMPLE  I. 

The  first  number  to  be  placed  in  the  second  Departure  Co- 
lumn is  20.74  ;  to  this  add  45.12,  and  it  makes  65.86,  for  the 
second  number;  to  45.12  add  75.16,  and  it  makes  120.28,  for 
the  third  number ;  to  75.16  add  84.72,  and  it  makes  159.88  for 
the  fourth  number  ;  to  84.72  add  84.72,  and  it  makes  169.44 
for  the  fifth  number;  to  84.72  add  44.77,  and  it  makes  129.49 
for  the  sixth  number;  to  44.77  add  21.02,  and  it  makes  65.79 
for  the  seventh  number;  to  21.02  add  0.0,  and  it  makes  21.02 
for  the  eighth  number* 


SURVEYING.  60 

6.  When  the  work  is  thus  far  prepared,  multiply  the  several 
numbers  in  the  second  Departure  column  by  the  northings  or 
southings  standing  against  them  respectively ;  place  the  pro- 
ducts of  those  multiplied  by  the  northings  in  the  column  of 
north  areas,  and  of  those  multiplied  by  the  southings  in  the  co- 
lumn of  south  areas ;  add  up  these  two  columns  and  subtract 
the  less  from  the  greater ;  the  remainder  will  be  double  the 
area  of  the  field  in  square  rods  or  square  chains  and  links, 
whichever  measure  was  used  in  the  survey. 


Fig.  63. 


Demonstration  of  ike  preceding  Rules. 
See  Fig.  63.  and  EXAMPLE  1. 


5 ... ,    H 

The  dotted  line  A  2  represents  the  northing,  and  the  line 
the  easting  made  by  the  first  course ;  these  multiplied  together, 
that  is,  77.15X20.74=1600.0910,  which  is  double  the  area  of 
the  triangle  A2B,  as  is  evident  from  the  Rule  to  find  the  area  of 
a  triangle,  PROB.  IX.  Rule  1.  This  number  is  to  be  placed  for 
the  first  number  in  the  column  of  north  areas.  The  line  3C 
represents  the  sum  of  the  eastings  made  by  the  first  and  second 
courses,  which  is  45. 12  the  second  number  in  the  first  departure 
column ;  if  to  this  you  add  20.74  the  length  of  the  line  2B  you. 
have  65.86,  which  is  the  second  number  in  the  second  depar- 
ture column,  and  which  represents  the  sum  of  the  two  lines  3C 
and  2B.  These  two  lines  with  the  line  2,  3  which  represents 
the  northing  made  by  the  second  course,  and  the  line  BC,  one 
of  the  sides  of  the  field,  form  a  Right  Angled  Trapezoid.  Now, 
by  the  rule  to  find  the  area  of  such  a  Trapezoid,  See  PROB.  X. 
65.86X31.66=2085.1276,  double  the  area  of  the  Trapezoid 
2  BC  3.  Place  this  product  for  the  second  number  in  the  co- 
lumn of  north  areas. 

Q 


66  SURVEYING. 

To  th£  line  3C  add  CD  30.04,  the  easting  made  by  the  third 
course,  and  you  have  75.16.  which  is  the  sttm  of  the  eastings 
made  by  the  three  first  courses,  and  the  third  number  in  the 
first  departure  column.  To  this  add  9.56,  the  easting  of  the 
fourth  course,  and  you  have  84.72,  the  length  of  the  line  IE, 
which  represents  the  sum  of  the  eastings  made  by  the  four  first 
courses,  and  is  the  fourth  number  in  the  first  departure  column, 
These  two,  viz.  the  lines  3D  75.16  arid  IE  84.72,  added  to- 
gether make  159.88,  the  fourth  number  in  the  second  departure 
column;  which,  being  multiplied  by  49.15,  the  length  of  the 
line  3,  1  which  represents  the  southing  made  by  the  fourth 
course,  will  give  double  the  area  of  the  Trapezoid  1  ED  3. 
The  number  thus  produced  is  7858.1020,  which  is  to  be  placed 
for  the  first  number  in  the  column  of  south  areas. 

The  fifth  course  being  due  south,  it  is  evident  the  sum  of  the 
eastings  will  remain  the  same  as  at  the  end  of  the  fourth 
course  ;  that  is,  the  line  4F  equals  the  line  IE,  which  is  84.72. 
These  added  make  169.44,  the  fifth  number  in  the  second  de- 
parture column.  This,  being  multiplied  by  54.10,  the  length 
of  the  line  EF,  which  is  the  southing  of  the  fifth  course  as  cor- 
rected in  balancing,  and  the  same  as  the  line  1,  4 — will  give 
double  the  area  'of  the  parallelogram  1  EF  4,  which  is 
9166.7040,  the  second  number  in  the  column  of  south  areas. 

From  the  line  AF  84.72  subtract  39.95,  which  is  a  west 
course,  and  it  leaves  4G  44.77,  the  sum  of  the  eastings,  or  the 
Meridian  distance,  at  the  end  of  the  bixth  course,  and  the  sixth 
number  in  the  first  departure  column.  From  this  subtract  23.75 
the  westing  made  by  the  seventh  course,  and  you  have  21.02, 
the  length  of  the  line  511,  which  is  the  Meridian  distance  at  the 
end  of  the  seventh  course,  and  the  seventh  number  in  the  first 
departure  column.  The  line  4G  44.77  added  to  the  line  511 
21.02  make  65.79,  the  seventh  number  in  the  second  departure 
column.  This  being  multiplied  by  32.21,  the  length  of  the 
line  4,  5 — which  is  ;tlie  southing  of  the  seventh  course,  will 
give  double  the  area  of  the  Trapezoid  4GH5,  which  is  2119* 
,0959,  the  third  number  in  the  column  of  south  areas. 

The  line  H5,  21.02,  is  the  westing  of  the  last  course,  and 
the  last  number  in  the  second  departure  column.  This  being 
multiplied  by  26.65,  the  length  of  the  line  5  A,  and  the  northing 
of  the  last  course,  produces  560.1830,  which  is  double  the  area 
of  the  Triangle  ASH,  and  the  last  number  in  the  column  of 
north  areas. 

JVofe.  It  will  be  observed  that  against  the  third  and  sixth  Courses  there 
are  no  Areas ;  the  reason  is,  that  these  Courses  being  one  east  and  the 


SURVEYING.  §7 

otter  west,  there  is  no  northing  or  southing  to  be  multiplied  into  them  : 
regard  can  therefore  be  had  to  them  only  in  forming  the  Departure  Co- 
lumns. 

By  inspecting  the  Figure,  and  attending  to  the  preceding 
illustrations,  it  will  be  seen  that  the  three  North  Areas  repre- 
sent double  the  Area  of  the  Triangle  A2B,  the  Trapezoid  2BC3, 
and  the  Triangle  A5H,  all  of  which  are  without  the  boundary 
lines  of  the  field :  also,  that  the  three  South  Areas  represent 
double  the  Area  of  the  Trapezoid  3DElvthe  Parallelogram 
1EF4,  and  the  Trapezoid  4GH5  ;  and  that  these  include  not  only 
the  field  but  also  what  was  included  in  the  North  Areas.  There- 
fore the  North  Areas  subtracted  from  the  South,  the  remainder 
will  be  double  the  Area  of  the  field,  contained  within  the  black 
lines. 


Additional  Directions  and  Explanations. 

The  northings  and  southings  may  be  added  and  subtracted 
instead  of  the  eastings  and  westings;  then  there  will  be  two 
Latitude  columns  instead  of  Departure  columns,  and  the  num- 
bers in  the  second  Latitude  column  must  be  multiplied  into 
the  eastings  and  westings,  and  you  will  have  east  and  west 
Areas. 

When  the  course  is  directly  north  or  south,  the  distance  must 
be  set  in  the  north  or  south  column ;  when  east  or  west,  in  the 
east  or  west  column.  There  will  therefore  sometimes  be  no 
number  to  be  added  to  or  subtracted  from  the  number  last  set 
in  the  Latitude  or  Departure  column ;  then  the  number  last 
placed  in  the  column  must  be  brought  down  and  set  against  such 
Course ;  as  in  EXAMPLE  I.  at  the  5th  Course.  It  may  also 
sometimes  be  the  case  that  there  will  be  no  number  to  multiply 
into  the  number  in  the  second  Latitude  or  Departure  column ; 
then  that  number  must  be  omitted,  and  against  such  Course 
there  will  be  no  Area  as  in  EXAMPLE  I.  at  the  3d  and  6th 
Courses. 

When  the  northings  or  southings,  eastings  or  westings,  be- 
ginning at  the  top,  will  not  admit  of  a  continual  addition  of  the 
one  and  subtraction  of  the  other,  without  running  out  before  you 
get  through  the  several  Courses,  you  may  begin  at  such  a  Course 
as  will  admit  of  a  continual  addition  and  subtraction ;  and  when 
you  get  to  the  bottom  go  to  the  top,  and  you  will  end  in  cipher 


68  SURVEYING. 

at  the  Course  next  above  that  where  you  began ;  as  in  EXAMPLK 
II.  which  begins  at  the  9th  Course  to  add  the  eastings  and  sub- 
tract the  westings. 


EXAMPLE  II. 


HO. 

Courses. 

Dist. 
Rods 

N. 

S. 

E. 

W. 

ldep.'2dep. 
Col.j  Col. 

North 
Areas 

South 
Areas 

1 

2 
3 
4 
5 
6 
6 
8 
9 
10 
11 
12 
13 

N.  75°0'E. 
N.2030E. 
East 
S.  33  SOW. 
S.  76  0  W. 
North 
S.  84  OW. 
N.5315W. 
N.3645  E. 
N.2230  E. 
S.  7646  E. 
S.  15  OW. 
S.  1645W. 

54.8'l4.2 
41.238.6 
64.8  
141.2  
64    1  
36    36 
46.41  
46.427.8 
76.8:61.5 
56     51.7 
48     
43.4!  
I  40.51  

152.9 
114.4 
164.8 
117.7|.  .  . 
15.5  .  .  . 

77.9 
62.1 

144.1 
158.5 
223.3 
145.4 
83.3 
83.3 
37.2 
0.0 
46 
67.4 
114.1 
102,9 
91.2 

235.3 
302.6 
381.8 
368.7 
228.7 
166.6 
120.6 
37.2 
46 
113.4 
181.5 
217 
191.1 

3341.26 
11680.36 



43395.99 
3544.85 

5997.60 

49 

... 

46 

<•>!  /J 

46.1 
37.2 

590.45 

1034.16 
2829 
5862.78 

11 

41.9 

38.8 

46.7 

11.2 
11.7 

1996.50 
9092.30 
7531.08 

Area  110  Acres,  2  Roods,  23  Hods. 

In  the  above  EXAMPLE  you  might  begin  at  the  4th  Course  to  add  tie 
westings  and  subtract  the  eastings ;  or  at  the  6th  Course  to  add  the 
northings  and  subtract  the  southings :  or  at  the  llth  Course  to  add  the 
southings  and  subtract  the  northings.  So  in  every  survey,  some  place 
may  be  found  where  you  may  begin  to  add  and  subtract,  without  run- 
ning out  before  you  get  through  all  the  Courses. 

When  a  field  is  very  irregularly  shaped,  it  will  often  happen 
that  parts  of  the  same  Area  will  be  contained  in  several  differ- 
ent products  In  the  columns  of  Areas ;  but  in  the  final  result, 
one  column  being  subtracted  from  the  other  will  leave  what  is 
included  within  the  boundary  lines  of  the  field. 


PURVEYING. 


Fig,  64. 


DEMONSTRATION. 
See  Fig.  64,  and  EX- 
AMPLE II. 


The  Area  standing  against  the  9th  Course,  which  is  where 
the  calculation  begins,  is  the  Triangle  12 K,  all  without  the 
Field. 

The  Area  against  the  10th  Course  is  the  Trapezoid  2KL8, 
also  without  the  Field. 

The  Area  against  the  llth  Course  is  the  Trapezoid  4ML3. 
This  is  a  South  Area,  and  contains  a  part  of  the  Field  and  also 
part  of  the  preceding  North  Area. 

The  Area  against  the  12th  Course  is  the  Trapezoid  5NM4, 
part  within  and  part  without  the  Field. 

The  Area  against  the  13th  Course  is,  the  Trapezoid  6AN5, 
part  within  and  part  without  the  Field. 

TKe  Area  against  the  1st  Course  is  the  Trapezoid  6AB7, 
part  within  and  part  without  the  Field.  This  is  a  North  Area, 
and  to  be  ultimately  subtracted  from  the  South  Areas  ;  but  this 
includes  a  part  of  the  preceding  South  Area,  viz.  the  space 
uAso ;  it  will,  however,  be  seen  hereafter  that  this  same  space 
is  included  in  another  South  Area.  This  North  Area  contains 
also  a  part  of  the  first  North  Area,  viz.  the  space  6no7 ;  but 
the  same  space  is  also  included  in  another  South  Area. 

The  Area  against  the  2d  Course  is  also  a  North  Area,  and  is 
the  Trapezoid  7BC8.  This  Trapezoid  contains  the  space 
sBCx,  without  the  Field ;  the  space  osxw,  within  the  Field ; 
and  the  space  7ow8,  without  the  Field.  But  the  space  osxw 
will  be  contained  in  the  next  south  Area ;  and  the  space  7ow8, 
which  was  contained  in  the  two  first  North  Areas,  will  be  con- 
tamed  in  the  next  South  Area. 

By  examining  the  whole  Figure  in  this  manner,  it  will  be 
seen  that  the  North  Areas  contain  all  without  the  Field  that  is 

R 


70  SURVEYING. 

taken  into  the  Calculation,  and  some  of  it  twice  over ;  they 
also  contain  part  of  the  Area  within  the  Field.  The  South 
Areas  contain  all  within  the  Field,  and  all  without  the  Field 
that  is  contained  in  the  North  Areas.  They  also  contain, 
twice  over,  so  much  of  the  Field  as  is  included  in  any  of  the 
North  Areas ;  and  likewise,  twice  over,  that  part  without  the 
Field  which  is  contained  twice  in  the  North  Areas.  So  that  sub- 
tracting the  North  from  the  South  Areas  leaves  double  the  Area 
of  the  Field. 

This  method  of  calculating  the  Area  of  a  Field  by  the 
Northings,  Southings, Eastings,  and  Westings,  divides  the  Field, 
with  a  certain  quantity  of  the  adjoining  ground,  into  Right  An- 
gled Triangles,  Right  Angled  Trapezoids,  Parallelograms,  or 
Squares,  as  may  be  seen  by  the  Figures.  It  may  therefore 
with  propriety  be  called  RECTANGULAR  SURVEYING. 


A  USEFUL  PROBLEM. 

To  find  the  true  Jlrea  of  a  Field  which  has  been  measured  by  a 
Chain  too  long  or  too  short. 

Calculate  the  Area  as  if  the  Chain  was  of  a  true  length,  then 
institute  the  following  Proportion  : 

As  the  Square  of  the  length  of  the  true  Chain ; 

Is  to  the  Area,  as  found  by  the  Cham  made  use  of; 

So  is  the  Square  of  the  length  of  that  Chain; 

To  the  true  Area  of  the  Field. 

EXAMPLE. 

.  Suppose  a  Field,  measured  by  a  Two  Rod  Chain  3  Inches 
too  long,  is  found  to  contain  41  Acres  1  Rood  and  33  Rods, 
what  is  the  true  Area  ? 

As  the  Square  of  33  Feet,  the  true  length  of  a  Two  Rod 
Chain ;  Is  to  41  Acre.s  1  Rood  and  33  Rods ;  So  is  the  Square 
of  33  FeetB  Inches,  the  length  of  the  Chain  used  in  the  Sur- 
vey; To  42  Acres  and  13  Rods.  33  Feet=396  Inches. 
396  X  396=156816  Square  Inches. 

41  Acres  1  Rood  33  Rods=6633  Rods. 

33  Feet  3  Inches=399  Inches.  399  x  399=159201  square 
inches* 

J59201  X  6633-7-156316=6733  Rods. 

6733~-160=42  Acres  13  Rods,  the  true 


SURVEYING,  71 

PART  II 

LAYING  OUT  LAND. 

PROBLEM  I.  To  lay  out  any  number  of  Acres  in  the  form 
of  a  Square. 

Annex  5  Ciphers  to  the  number  of  Acres,  which  will  turn 
them  into  Square  Links,  the  Square  Root  of  which  will  be  the 
Side  of  the  Square  in  Links. 

EXAMPLE.  It  is  required  to  lay  out  810  Acres  in  the  form  of  a 
Square. 

Answer.  Each  Side  of  the  Square  must  be  9000  Links,  or 
90  Chains. 

PROBLEM  II.  To  lay  out  any  number  of  Awes  in  the  form, 
of  a  Parallelogram,  whereof  one  Side  is  given. 

Divide  the  number  of  Acres,  when  turned  into  Square  Links, 
by  the  given  Side  ;  the  Quotient  will  be  the  Side  required. 

EXAMPLE.  What  must  be  the  longest  side  of  a  Parallelogram, 
which  is  to  contain  25  Acres,  when  the  shortest  side  is  6 
Chains  and  50  Links  1 

Answer.  2500000-7-650=4545  Links  for  the  longest  Side. 

PROBLEM  III.  To  lay  out  any  number  of  Acres  in  a  Field, 
3,  4,  5,  6,  fyc.  times  as  long  as  it  is  broad. 

Divide  the  Acres,  when  turned  into  Square  Links,  by  the 
proportion  between  the  length  and  breadth ;  the  Square  Root 
of  the  Quotient  will  be  the  shortest  Side. 

EXAMPLE.  It  is  required  to  lay  out  100  Acres  5  times  as  long 
as  it  is  broad. 

Answer.  10000000-j-5=;2000000  the  Square  Root  of  which 
is  1414  Links  for  the  shortest  Side,  and  the  longest  will  be  7070 
Links. 

PROBLEM  IV.  To  make  a  Triangle  which  shall  contain  a 
given  number  of  Acres,  being  confined  to  a  certain  Base. 

Double  the  given  number  of  Acres,  to  which,  annex  5  Ci- 
phers, and  divide  by  the  Base  ;  the  Quotient  will  be  the  Per- 
pendicular in  Links. 

EXAMPLE.  Upon  a  Base  of  40  Chains  to  lay  out  100  Acres  in 
a  Triangular  form. 

Answer.  5000  Links  or  50  Chains  will  be  the  length  of  the 
Perpendicular. 


SURVEYING. 


Fig.  55. 


The  Perpendicular  may  be  erected 
from  any  part  of  the  Base :  Thus,  the 
Triangle  ABC.  -See  Fig.  55.  is  the 
same  as  ABE,  each  containing  100 
Acres. 


When  the  given  Base  is  so  situa- 
ted that  a  Perpendicular  of  suffi- 
cient length  cannot  be  erected  there- 
from, continue  the  Base  as  from  B  to 
D.  Fig.  56.  from  which  erect  the 
Perpendicular  DC,  and  complete 
the  Triangle  ABC,  which  will  con- 
tain 100  Acres. 


Fig.  56. 


L. — IB 


PAUT  III. 

DIVIDING  LAND. 

As  different  r  ielcls  are  so  variously,  and  many  of  them  irre-. 
gularly  shaped,  and  as  they  are  required  to  be  divided  in  many 
different  proportions,  it  is  difficult  to  give  Rules  which  will  ap- 
ply to  particular  cases.  The  business  of  dividing  Land  must 
therefore  be  left,  in  a  great  measure,  to  the  skill  and  judgment 
of  the  Surveyor ;  who,  if  he  is  well  acquainted  with  Trigono- 
metry, and  with  measuring  Land,  will  not  find  it  difficult,  after 
a  little  practices,  to  divide  a  Field  in  such  a  manner  as  shall  be 
desired.  If  he  has  before  him  a  plot  of  the  Field,  and  knows 
the  number  of  parts  into  which  it  is  to  be  divided,  and  the  pro- 
portion which  each  part  is  to  bear  to  the  others,  he  will  readily 
find  out  where  the  dividing  Lines  are  to  DC  drawn. 

A  few  RULES  and  EXAMPLES  will  be  given  for  the  general 
instruction  of  the  Learner. 

PROBLEM  I.  To  cut  off  any  number  of  Acres  from  a 
or  *  Parallelogram . 


SURVEYING. 


73 


Say,  as  the  whole  number  of  Acres  in  the  Field  ;  Is  to  the 
length  of  the  Square  or  length  or  breadth  of  the  Parallelo- 
gram ;  So  is  the  number  of  Acres  proposed  to  be  cut  off;  To 
their  proportion  of  the  length  or  breadth. 

PROBLEM  II.  To  cut  off  any  number  of  Acres  by  a  Line 
proceeding  from  any  Jingle  of  a  Triangle. 

Measure  the  Base,  or  Side  opposite  the  Angle  from  which 
the  dividing  Line  is  to  be  drawn;  Then  say,  As  the  number 
of  Acres  in  the  whole  Triangle  ;  Is  to  the  whole  Base ;  So  is 
the  given  number  of  Acres ;  To  their  part  of  the  Base. 

Fig.  57. 


EXAMPLE.     See  Fig.  57. 


In  the  Triangle  ABC,  which  contains  48  Acres,  it  is  required 
to  cut  off  18  Acres,  by  a  Line  proceeding  from  C  to  the  "Base 
/V.B,  which  is  40  Chains. 

As  48  :  40  :  :  18  :  15 

Lay  45  Chains  on  the  Base  from  B  to  D,  and  draw  the  Line 
CD.  The  Triangle  will  then  be  divided  as  was  proposed  ; 
BCD  containing  18  Acres. 

PROBLEM  III.  To  take  off  any  given  number  oj  Acres  from 
a  multangular  Field. 

Fig.  65. 


EXAMPLE  I.  See  Fig.  65. 


Let  ABCD,  &c.  be  the  Plot  of  a  Field  containing  11  Acres, 
from  which  it  is  required  to  cut  off  5  Acres. 

Join  two  opposite  Corners  of  the  Field  as  D  and  G,  with  the 


R 


V4  SURVEYING. 

Line  DG  (which  you  may  judge  to  be  near  the  partition  Line) 
"and  find  the  Area  of  the  part  DEFG,  which,  suppose,  may 
Viant  140  Rods  of  the  quantity  proposed  to  be  cut  off.  Mea- 
sure the  Line  DG,  which,  suppose  to  be  70  Rods ;  divide  140 
by  35  the  half  of  DG,  and  the  Quotient  4  will  be  the  length  of 
a  Perpendicular  whose  Base  is  70  and  the  Area  140.  Lay  oft' 
4  Rods  from  G  to  I,  and  draw  the  Line  DI,  which  will  be  the 
dividing  Line, 


EXAMPLE  If.     See  Fig.  GO. 


Let  ABCD,  &c.  be  a  tract  of  land 
to  be  divided  into  two  equal  parts,  by 
a  line  from  I  to  the  opposite  side  CD ; 
to  find  arithmetically  on  what  part  of 
the  line  CD  the  dividing  line  IN  will 
fall :  or  to  find  the  Distance  CN. 


FIELD  BOOK. 

Rods. 

AB.  N. 

19°  0' 

E. 

103 

GF. 

BC.    S. 

77    0 

E. 

91 

GH 

CD.   S. 

27    0 

E. 

115 

HI. 

DE.    S. 

52    0 

W. 

58 

IA. 

EF.    S. 

15  30 

E. 

76 

Rods, 

st  70.9 

GH.  N.  36°  0'    W.  47 
North  64.3 

N.  62  15     W.  59 
Acres  Rood  Rods 
Whole  Area  152—1  —  25 

Find  the  Area  of  the  part  I  ABC  I,  according  to  SECTION  III, 
Pa*e  57,  as  follows  :  set  the  Latitude  and  Departure  of  the  three 
first  Sides,  IA,  AB,  and  BC,  in  their  proper  columns,  in  a  Tra 
verse  Table  ;  and  place  as  much  southing,  vbt,109.1,  equal  to 
the  line  CK,  and  as  much  westing,  viz.  71.7,  equal  to  the  line 
KI,  as  \vill  balance  the  columns.  This  southing  and  westing 
Will  be  the  Latitude  and  Departure  made  by  the  line  CI.  The 
Area  of  IABCI  will  be  found  to  be  8722  Rods,  which  is  less 


SURVEYING,  n 

than  half  the  Area  of  the  whole  Field  by  3470  Rods,  the  quan- 
tity to  be  contained  in  the  Triangle  TCN. 

Find  the  bearing  and  distance  of  CI  by  RIGHT  ANGLED  TRIGO- 
NOMETRY, CASE  IV.  as  follows  : 

As  CK,  the  southing  of  CI,  109  ^j,;    V^'   .-'-       -        -          2.03743 

:  Radius  -         -         -         10.00000 

:  :  KI,  the  westing  of  CI,  71.7      -        -        -         -  -    .    -        -          1.85552 

11.85552 
2.03743 


:  Tangent  Course  S.  33°  20'  W.       K^;i/;,T*;T  •  i^  "  :?  Ci  I     9-81809 

As  Sine  Course  33°  20          -         -         -        -   *"  -  \  '  -"'      -    '      9.73997 
:  Departure  KI  71.7     -  '  ;T •'•': "% •'  \*V>  - -P'J  ''  '.        -        -          1.85552 

::  Radius        •;'  , -r^V*  -ri«  •  :_--  <'•''-  [    '  •"'  -••-'•      -         -         10.00000 

11.85552 
9.73997 

:  Distance  1C  130        -        -        -  -  '     -  -          2.11555 


Jfote.  In  this  way  the  Course  and  Distance  may  be  found  from  one  Angle 

^)f  a  Field  to  another. 

i 

Having  found  the  line  CI,  divide  3470,  the  number  of  Rods 
to  be  contained  in  the  Triangle  ICN,  by  one  half  the  line  CI, 
viz.  65,  the  quotient  will  be  the  length  of  the  Perpendicular 
PN,  viz.  53.4. 

Now,  by  the  bearings  of  CI  and  CD,  it  appears  that  they 
form  an  Angle  of  600  20X ;  wherefore,  in  the  Triangle  CPN 
are  given  the  side  PN  53.4,  and  the  Angle  at  C  60°  20X,  to  find 
the  Hvpothenuse  CN. 

i 

As  Sine  PCN  60°  207  -         9.93898 

:  Side  PN  53.4  1.72754 

:  :  Radius          ....        10.00000 


11.72754 

9.93898 

:IIyp.  CN  61.5  1.78856 

Thus  the  dividing  line  m.ust  go  from  T  to  a  point  on  the  lino, 
CD,  which  is  61.5  Rods  from  C,     The  bearing  and  distance  of 


76  SURVEYING. 

this  line  may  be  found  by  the  directions  given  above  for  finding 
the  bearing  and  distance  of  the  line  CJ.  Or,  they  may  be  fount 
by  Oblique  Trigonometry,  CASE  III. 


Jfaother  Method  of  finding  the  Distance 

Having  ascertained  the  Latitude  and  Departure  of  the  line 
CI.  set  them  down  in  a  Traverse  Table  ;  find  the  Latitude  and 
Departure  of  the  line  CD,  and  place  them  in  the  Table  ;  the 
difference  between  the  northing  of  the  line  1C,  and  the  southing 
of  the  Line  CD  will  be  the  southing  of  the  line  DI,  viz.  6.6  ; 
and  the  sum  of  the  eastings  of  those  lines,  as  they  are  botli 
easterly,  will  be  the  westing  of  the  line  DI,  viz.  123.9.  Pro- 
ceed to  calculate  the  Area  of  the  Triangle  1CD,  which  will  be 
found  to  be  6522  Rods,  nearest. 

JY*ote.  As  in  this  Triangle  two  sides  and  their  contained  Angle  are  given, 
the  Area  may  be  found  by  PROS.  IX.  Rule  4,  Page  38. 

Having  found  the  Area  of  this  Triangle,  proceed  to  find 
CN according  to  PROB.  II.  Page  73,  as  follows: 

As  the  Area  of  the  Triangle ;  Is  to  CD  the  Base ;  So  is  the 
quantity  to  be  contained  in  the  Triangle  ICN;  To  CNits  pro- 
portion of  the  Base. 

As  6522:  115:  :  3470:  61.2 


Jl  third  method  of  finding  the  Distance  CJV*. 

-To  the  Logarithm  of  double  the  Area  to  be  contained  within 
the  Triangle  ICN  add  Radius;  from  this  Sum  subtract  the 
Logarithmic  Sine  of  the  angle  atC ;  and  from  the  Remainder  sub- 
tract the  Logarithm  of  the  Side  1C ;  the  last  Remainder  will  be 
the  Logarithm  of  the  Side  CN. 

The  double  Area  of  the  Triangle  ICN  is  6940 ;  the  Angle  at 
C  is  600  20';  the  Side  1C  is  130. 

Double  Area  6940  3.84136 

Radius  -  -      :^^'     *.VA       10.00000 


13.84136 

Sine  ICN  600  20'  -        >  V  '        9.93898 


3.90238 


SURVEYING.  ,7.7 

3.90238 
Side  1C  130  -          -          -          2.11394 


Side  CN  61.5       },**i  'i'^','  £*-*       1.78844 


"of*.  Radius  may  be  added  by  placing  a  Unit  before  the  Index  of.  th.e 
Logarithm  for  the  double  Area,  without  the  trouble  of  setting  down 
the  Ciphers; 


%  Natural  Sines. 

Divide  the  Double  Area  by  the  Natural  Sine  of  the  given 
Angle,  and  that  quotient  by  ihe  given  Side ;  the  last  Quotient 
will  be  the  Side  CN. 

Nat.  Sine  of  the  Angle  at  C  60°  20'    0.86892 

6940-U).86892=7986.92 

7986.92-f-130=61.43 


From  the  above  the  following  general  Rule  may  be  drawn, 

To  find  the  Side  of  a  Triangle  when  the  Area  is  given,  with 
one  of  the  Sides  and  the  Angle  contained  between  the  given  Side 
and  the  Side  required. 

To  the  Logarithm  of  double  the  Area  add  Radius;  from 
this  Sum  subtract  the  Logarithmic  Sine  of  the  given  Angle, 
and  from  the  Remainder  subtract  the  Logarithm  of  the  given 
Side;  the  last  Remainder  will  be  the  Logarithm  of  the  Side 
required* 

Or,  By  Natural  Sines:  Divide  the  double  Area  by  the  Nat. 
Sine  of  the  given  Angle,  and  that  Quotient  by  the  given  Side  ; 
the  last  Quotient  will  be  the  Side  required. 


CONCLUDING  REMARKS. 

Other  methods  of  surveying  Fields  are  taught  by  some 
authors  on  this  subject.  The  preceding,  however,  will  be 
found  most  useful  in  actual  practice.  Other  instruments  be- 
sides those  mentioned  in  this  Book  are  also  son  etimes  used.; 
such  as  the  Plain  Table,  Semicircle)  Perambulator,  Theodo- 


78  SURVEYING. 

lite,  &c.  But  of  these  instruments  very  little  use  is  made  m 
New-England  ;  and  they  are  not  often  to  be  met  with.  For 
general  practice  none  will  be  found  more  useful  than  a  common 
Chain,  and  a  Compass  upon  Rittenhouse's  construction.  A 
Surveyor  should  also  provide  himself  with  an  Offset  Staff,  ten 
Links  in  length,  and  accurately  divided  into  Links.  This 
should  be  made  of  firm  hard  wood,  and  will  be  found  very  con- 
venient in  taking  Offsets,  and  also  in  measuring  the  Chain ; 
which  should  "be  often  done,  as  from  a  variety  of  causes  a  Cham 
is  liable  to  become  inaccurate. 

It  will  be  observed  that  in  this  Work  there  are  no  descrip- 
tions of  Mathematical  and  Surveying  instruments.  The  Com- 
piler omitted  such  descriptions  from  a  belief  that  nothing  which 
can  be  written  on  the  subject  will  enable  a  person  to  under- 
stand them  without  an  actual  inspection  of  the  instruments 
themselves,  and  some  instruction  from  those  acquainted  with 
them. 

The  general  principles  here  taught  may  be  applied  to  the 
surveying  of  Townships,  Roads,  Rivers,  Harbours,  &c» 


APPENDIX. 


OF  THE    VARIATION  OP    THE    COMPASS  AND  ATTRACTION  OF  THE 
NEEDLE. 

THE  Variation  of  the  Compass  is  the  number  of  Degrees  that 
the  Magnetic  Needle  points  from  the  true  North,  either  East 
or  West.  This  differs  in  different  places,  and  in  the  same 
place  at  different  times.  It  is,  at  present,  in  Connecticut,  a 
iew  degrees  to  the  Westward.  That  is,  the  Needle  points  to 
the  Westward  of  North,  and  is  gradually  approaching  the  true 
North. 

The  following  method  of  ascertaining  the  Variation,  by  the 
North  Star,  has  been  adopted  by  many  Surveyors,  as  the 
most  eligible  to  be  practised  on  Land.  It  was  communicated 
to  the  Compiler  by  Moses  Warren,  Jun.  Esq.  of  Lyme,  an 
experienced  Surveyor,  with  permission  to  publish  it. 

The  Star  commonly  called  the  North  Star,  is  not  "directly 
North  but  revolves  round  the  Pole  in  a  small  circle,  once  in  24 
hours.  It  cannot  therefore  be  due  North  but  twice  in  that 
period ;  and  that  is  within  a  very  few  minutes  of  the  time 
when  a  Star,  called  JUioth,  in  the  Constellation  of  Ursa  Major, 
or  the  Great  Bear,  is  directly  over  or  under  it.  There  is  also 
another  Star  nearly  in  an  opposite  direction  from  the  Pole, 
called  Gamma,  in  the  Constellation  of  Cassiopeia.  When 
these  three  Stars  a.T«  vertical  the  North  Star  is  very  near  the 
Meridian ;  and  whe-a  they  are  horizontal,  it  is  at  its  greatest 
Elongation,  that  is,  at  its  greatest  distance  East  or  West  of  the 
Pole,  and  on  the  same  side  as  the  Star  in  Cassiopeia.  The 
Variation  may  be  calculated  when  the  Star  is  on  the  Meridian, 
or  when  at  its  greatest  Elongation ;  more  accurately,  however, 
at  the  latter  period,  because  its  motion  being  then  nearly  verti- 


BO 


APPENDIX. 


cal  for  some  time  gives  the  observer  a  better  opportunity  to 
complete  bis  observation.* 

To  find  the  Elongation  of  this  Star  in  any  Latitude,  its  DecKna-- 
tion  must  be  known;  that  is,  its  distance  North  of  the  Equator. 
This  being  found,  institute  the  following  Proportion : 

As  Co-Sine  of  the  Latitude;  Is  to  Radius;  So  is  Co-Sine  of 
the  Declination ;  to  Sine  of  the  Elongation. 

The  Decimation  of  the  North  Star,  January  1,  1810,  was 
880  17'  28",  and  increasing  at  the  rate  of  about  19  seconds  and 
one  half  annually. 

The  following  Table  Shows  the  Elongation,  in  several 
different  Latitudes,  for  5  years  successively.  It  is  calculated 
for  the  first  of  January  in  each  year ;  and  ki  using  it,  if  the  time, 
when  the  Elongation  is  required,  be  past  the  middle  of  the 
year,  take  it  for  the  beginning  of  the  next  year. 

Ji  Table  showing  the  Elongation  of  the  North  Star. 


Latitude. 

1820 

1821 

1822 

1823 

1824 

380 

20  5'  34" 

20  5'  7" 

20  V  39" 

20  4'  is// 

20  3'  47" 

39 

2  7  23 

2  6  54 

2  6  25 

2  5  59 

2  5  33 

40 

2  9  12 

2  8  41 

2  8  14 

2  7  46 

2  7  20 

41 

2  11  11 

2  10  40 

2  10  12 

2  9  44 

2  9  18 

42 

2  13  10 

2  12  39 

2  12  11 

2  11  43 

2  11  16 

43 

2  15  22 

2  34  51 

2  14  22 

2  13  54 

2  13  26 

44 

2  17  33 

2  17  4 

2  16  34 

2  16  5 

2  15  37 

*  The  following  Figure  exhibits  a  view  of  the  relative  situation  of  these 
Stars  as  they  appear,  when  in  a  horizontal  position  :  or  when  the  North 
Star  is  in  its  greatest  Eastern  Elongation* 

The  Great  Bear.  Cassiopeia. 

*  North  Star  ** 

*Alioth  Pole0  *  Gamma* 


APPENDIX.  || 

The  Elongation  for  the  Latitude  of  the  observation  being 
i  alculated,  or  taken  from  the  above  Table,  proceed  to  find  its 
range,  according  to  the  following  directions  ; 

Take  a  pole  18  or  20  feet  in  length;  to  the  end  of  it  fasten  a 
small  line ;  raise  it  to  an  elevation  of  45°  or  50° ;  and  support 
it  by  two  cratches  of  suitable  height  to  keep  it  firm  in  its 
place.  At  the  end  of  the  line,  near  the  ground,  fasten  a  weight 
of  half  a  pound  or  more,  which  should  swim  in  water  to  prevent 
the  air  from  moving  the  line.  Southward  of  the  line,  fix  a 
Compass  sight,  or  other  piece  of  metal  or  wood,  with  a  narrow, 
perpendicular  aperture  at  a  convenient  height  from  the  ground, 
say  about  2  or  2  1-2  feet ;  and  let  it  be  so  fixed  that  it  can  be 
moved  a  small  distance  East  or  West  at  pleasure.  Let  an  as- 
sistant hold  alight  either  NE.  or  NW.of  the  line,  nearly  as 
high  as  the  range  irom  the  sight  to  the  North  Star,  in  such  a. 
position  that  the  line  may  be  plainly  seen ;  then,  (the  three 
Stars  above  mentioned  being  parallel  or  nearly  so  with  the 
Horizon)  move  the  sight-vane  East  or  West,  until  through  the 
aperture,  the  line  is  seen  to  cut  the  Star;  and  continue  to  ob- 
serve, at  short  iniervals,  till  the  Star  is  seen  at  its  greatest 
Elongation.  Let  a  lighted  candle  be  placed  in  an  exact  range 
with  the  sight-vane  and  line  at  the  distance  of  20  Rods  or  more, 
which  should  stand  perpendicularly,  be  made  fast,  extinguished, 
and  left  till  morning.  Then  the  sight-vane,  the  line,  and  the 
candle,  will  be  the  range  of  Elongation,  which  observe  accu- 
rately with  a  Compass  ;  and  if  the  Elongation  be  East  and  the 
Variation  West,  the  former  must  be  subtracted  from  the  latter; 
and  if  they  are  both  West  they  must  be  added,  and  their  differ- 
ence or  sum  will  be  the  true  Variation. 


OF  THE  ATTRACTION  OF  THE  NEEDLE. 

Itis  well  known  that  any  iron  substance  has  an  influence  upon 
the  magnetic  Needle,  attracting  it  one  way  or  the  other  from 
the  point  where  it  would  settle,  were  there  no  such  attraction. 
A  surveyor  should  therefore  be  careful  to  see  that  no  iron  is 
near  the  compass  when  taking  a  bearing.  But  as  the  Earth  in 
certain  spots  contains,  near  its  surface,  iron  or  other  minerals 
which  attract  the  Needle,  it  will  frequently  happen  that  it  will 
point  wrong.  To  ascertain  whether  this  is  the  case,  the  sur- 
v  eyor,  at  each  station,  should  take  a  back  view  of  the  one  last 
left ;  and  if  he  finds  that  the  compass  does  not  reverse  truly,  IK 

S 


82  APPENDIX. 

may  be  sure,  provided  the  compass  be  accurately  graduated  anu 
placed  horizontally,  that  he  either  made  a  mistake  at  the  last 
station,  or  that  in  one  or  the  other  of  the  stations,  the  Needle 
was  attracted  from  the  true  point.  When  he  finds  a  place 
where  he  suspects  there  is  an  attraction,  he  should  go  a  few 
rods  backward  or  forward,  and  see  whether  the  Needle  points 
differently.  In  this  way  he  may  prevent  mistakes  in  his  field 
notes,  by  putting  down  a  wrong  course.  To  take  back  sights 
is  particularly  necessary  in  running  long  lines,  and  laying  out 
new  lands,  where  the  Needle  is  the  only  thing  to  guide  the  sur- 
veyor. 

By  practice  and  experience  a  knowledge  will  be  acquired  on 
this  subject,  and  with  regard  to  many  other  things  in  surveying, 
which  cannot  be  taught  by  books ;  and  after  all  the  directions 
which  can  be  written,  the  practitioner  will  frequently  find  oc- 
casion for  the  exercise  of  his  own  judgment. 


.2  Rule  to  find  the  difference  between  the  present  -variation  of  tht 
Compass,  and  that  at  a  time  when  a  Tract  was  formerly  sur- 
veyed, in  order  to  trace  or  run  out  the  original  lines. 

Go  to  any  part  of  the  premises  where  any  two  adjacent  cor- 
ners are  known  ;  and  if  one  can  be  seen  from  the  other,  take 
their  bearing  ;  which,  compared  with  that  of  the  same  line  in 
the  former  survey,  shows  the  difference.  But  if  one  corner 
cannot  be  seen  from  the  other,  run  the  line  according  to  the 
given  bearing,  and  observe  the  nearest  distance  between  the  Jin? 
so  run  and  the  corner ;  then  work  by  the  following  proportion  • 

As  the  length  of  the  whole  line, 

Is  to  57.3  degrees,* 

So  is  the  said  distance, 

To  the  difference  of  variation  required. 

EXAMPLE. 

Suppose  it  be  required  to  run  a  line,  which,  some  years  ago, 
bore  N.  45°  E.,  distance  20  chains,  and  in  running  this  line  by 
the  given  bearing,  the  corner  is  found  20  links  to  the  left  hand  : 
what  is  the  present  bearing  of  this  line  1 

*  57.3  degrees  is  the  Radius  of  a  circle  (nearly)  in  such  payls1  as  the  cir- 
contains  360. 


APPENDIX.  83 

Ch.         Deg.         L, 
As  20     :     57.3  :  :  20 
100  20 

2000     1146.0 
60 

2000)68760(34  Minutes. 

Answer-r-34  Minutes  to  the  left  hand  is  the  allowance  re 
-juired,  and  the  line  in  question  bears  N.  44°  26'  E. 


The  compiler  of  this  work  acknowledges  himself  under  ob- 
ligations to  George  Gillett,  Esq.  Surveyor  General  of  the  state 
of  Connecticut,  for  the  following  illustrations,  remarks,  and 
miscellaneous  questions,  considering  them  calculated  to  be  use- 
ful to  the  learner,  and  the  practical  surveyor.  They  came  to 
hand  too  late  to  be  inserted  in  their  proper  places,  in  the  body 
of  the  work,  and  are  here  put  together  in  the  Appendix. 


Remarks  on  the  Irregularities  of  the  Magnetic  Ntedle. 

By  a  statute  of  this  state,  applicants  for  the  appointment  of 
County  Surveyor  are  required  to  be  well  skilled  in  point  of 
science  in  the  theory  of  the  most  approved  methods  of  survey- 
ing lands.  It  is  also  as  necessary  that  they  should  be  as  well 
skilled  in  practical  surveying.  A  practical  knowledge  must  be 
acquired  by  experience,  and  no  one  can  have  a  thorough  know- 
ledge of  correct  practice  without  being  made  acquainted  with 
the  imperfections  and  irregularities  of  the  Magnetic  Needle. 

It  is  supposed,  by  most  people,  that  this  instrument,  in  all 
places,  points  directly  to  the  Poles  of  the  earth,  and  that  it  re- 
mains as  permanent  as  the  Poles  themselves — an  infallible 
guide.*  This  is  a  mistaken  idea.  A  few  remarks  on  this  sub- 

*  There  is  one  line  around  the  globe  on  which  there  is  no  variation.  The 
general  course  of  this  line,  on  this  side  of  the  globe,  is  from  northwest  to 
southeast,  but  is  crooked  and  irregular  in  its  course.  According  to  Dr. 
Holly's  chart,  made  in  1700,  the  line  of  no  variation  crossed  the  meridian 
of  London  in  55°  South  latitude — crossed  the  equator  in  17°  W.  longi- 
tude—from  thence,  by  various  windings,  to  the  island  of  Bermuda,  from 


y  APPENDIX. 

ject  will  here  l>e  offered,  and  some  facts  respecting  it  will  be 
slated. 

Notwithstanding  the  great  utility  derived  from  the  Magnetic 

thence  nearly  a  west  course  until  it  struck  the  continent  near  Charles- 
ton, in  South  Carolina.  This  fine  is  not  stationary,  but  is  ever  varying 
its  position  ;  and,  notwithstanding  the  irregularity  of  its  courses,  it 
never  crosses  itself.  .  About  1756,  another  variation  chart  was  made,  when 
it  was  found  that  the  line  had  fallen  so  far  to  the  west  that  it  struck  the  con- 
tinent near  the  coast  of  Florida.  On  the  east  side  of  this  line,  the  Magnetic 
Needle  points  to  the  west  of  north,  and  on  the  west  side  it  points  to  the 
east  of  north,  and  a  regular  increase  of  either  east  or  west  variation  is  found 
from  it,  depending  on  the  course  that  is  taken.  The  line  of  no  variation 
now  runs  through  Pennsylvania,  and  not  far  from  Norfolk,  in  Virginia. 
When  the  Connecticut  Western  Reserve  was  survey.ed  into  townships,  the 
variation  at  that  place  was  easterly  from  one  to  two  degrees.  In  1813,  at 
New-Orleans,  the  variation  was  easterly,  about  eight  or  nine  degrees.  In= 
1701,  at  Philadelphia,  the  variation  was  westerly,  eight  degrees  and  a  half. 
In  1794,  at  the  same  city,  the  west  variation  had  diminished  to  one  degree  and 
a  half,  which  proves  that  the  progress  of  the  line  of  no  variation  had  been 
from  west  to  east.  -In  1813,  by  observations  at  this  city,  it!  was  found  that 
the  west  variation  had  increased  to  about  two  or  three  degrees.  By  a  series 
of  observations,  commenced  at  Hebron  in  Connecticut,  by  the  writer  of  this, 
in  1805,  and  continued  to  1813,  it  was  found  that  the  west  variation  during 
that  period  increased  more  than  half  a  degree.  The  result  of  these  obser- 
vations agree  with  those  at  Philadelphia,  that  there  had  been  a  retrograde 
motion  of  the  Needle.  Since  1313,  the  west  variation  has  diminished,  01- 
certainly  it  has  not  increased.  The  west  variation  at  Hebron  is  now  (1325) 
a  few  minutes  more  than  five  degrees.  In  1680,  at  London,  the  Magnetic 
Needle  pointed  eleven  degrees  and  a  half  to  the  east  of  north,  which  proves 
that  the  line  of  no  variation  was  east  of  that  place.  The  east  variation 
diminished  until  1657,  when  the  line  of  no  variation  arrived  there  and  sooji 
passed  by ;  of  course  west  variation  began,  and  continued  to  increase  until 
1806,  when  it  exceeded  twenty-four  degrees. 

The  line  of  no  variation  must  have  had  a  rapid  progress  through  the  At- 
lantic and  through  a  great  part  of  the  United  States,  to  have  arrived  at 
Charleston  in  1700,  and  at  the  coast  of  Florida  in  1756.  The  present  bear- 
ing of  all  old  lines  in  this  state  prove  that  there  has  been  a  considerable  de- 
crease of  west  variation  since  the  first  surveys  were  made  ;  which  also  proves 
that  the  progress  of  the  line  of  no  variation,  in  the  United  States,  has,  for 
a  long  time,  been  from  west  to  eas.t.  How  far  the  line  of  no  variation  pro- 
gressed westward  in  the  interior  of  this  country  before  it  turned,  no  one  can 
tell.  It  is  unaccountable  how  the -west  variation  in  London  should  increase, 
while  at  Philadelphia  it  was  diminishing,  when  both  places  are  on  the  same 
side  of  the  line  of  no  variation.  The  variation  of  the  Needle  has  long  been 
a  subject  of  much  perplexity.  Observations  have  been  made  in  abundance. 
Many  facts  have  been  ascertained,  but  the  difficulty  is,  they  are  not  reducible 
to  system.  The  polarity  of  the  Magnetic  Needle,  with  its  variations  and 
irregularities,  is  a  hidden  mystery,  which  is  never  to  be  searched  out  by  man. 
It  is  sufficient  in  itself,  without  any  other  evidence,  to  cause  the  reflecting 
mind  to  wonder  at,  admire,  and  adore  the  wisdom,  knowledge,  and  powet 
of  HIM  who  planned  and  directs  it» 


APPENDJX.  8# 

.Needle,  it  caniiot  be  relied  on  where  great  accuracy  is  requiredj 
on  account  of  the  irregularities  to  which  it  is  subject,  such  as 
its  annual  motion  in  variation,  its  diurnal  motion,  and,  what  is 
attended  with  greater  difficulty,  its  local  attraction.  When  an 
old  course  is  given  to  renew  a  line,  it  cannot  be  depended  on, 
un  account  of  the  difference  in  variation  between  the  time  of 
the  first  running  and  the  renewal  of  it. 

No  annual  rate  can  be  fixed  on  for  the  variation  of  the  Mag- 
uetic  Needle,  as  its  motion  is  much  more  rapid  in  some  years 
than  in  others.  By  observations  made  at  London  during  a  pe- 
riod of  more  than  two  hundred  years,  it  appears  that  in  some 
years  the  motion  of  the  Needle  was  rapid,  in  others,  but  little 
would  be  discovered,  and,  in  some  years,  the  motion  was  retro- 
grade. There  is  no  regularity  in  its  motion  in,  any  place. 

Another  difficulty  in  retracing  a  line  from  an  old  course  or 
from  one  recently  given  is,  that  it  is  often  found  that  two  com- 
passes do  not  make  the  same  course.  It  was  well  known  to  the 
celebrated  Rittenhouse,  that  his  compasses  did  not  all  agree,  or 
make  the  same  course,  and  he  never  was  satisfied  as  to  the  rea- 
-•on  of  it.  It  has  also  been  ascertained  that  different  Needles 
do  not  point  alike  at  the  same  place.  French  writers,  on  Mag- 
netism, have  lately  treated  on  this  subject.  Two  compasses 
may  differ  a  quarter  of  a  degree  or  more  or  less,  when  no  de- 
fect can  be  discovered  in  either^  A  survey  may  be  taken  as 
correctly  with  one  as  with  the  other.  The  question  then  natu- 
rally arises,  which  of  the  two  is  right  ?  The  answer  is,  both 
are  right ;  neither  of  them  points  directly  to  the  Poles  of  the 
oarth,  except  on  the  line  of  no  variation.  All  that  can  be  said 
of  them  is,  that  one  has  a  greater  variation  than  the  other,  and 
that  which  has  the  least  'cannot  have  the  preference..  The  di- 
urnal motion  of  the  Magnetic  Needle  is  another  defect  in  it, 
As  the  sun  rises  in  the  forenoon,  and  the  earth  becomes  heated, 
it  has  an  effect  on  the  unknown  something  which  gives  polarity 
to  the  Needle,  and  turns  the  north  end  of  it  to  the  west  In 
the  afternoon  and  night  following,  it  returns  to  its  position.. 

For  several  years,  the  writer  of  this  made  observations  with. 
Hittenhouse's  compass,  to  ascertain  the  diurnal  motion  ;  and  ia 
(he  summer  season  usually  found  about  a  sixth  part  of  a  degree. 
In  the  winter,  but  little  or  none  could  be  discovered.  The  di- 
urnal motion  of  the  Needle  has  been  known  in  Europe  about  a 
century.*  The  local  attraction  is  an  irregularity  to  which  the 
Magnetic  Needle  is  subject.  These  are  found  oftener  in  hilly, 

*  The  cl'iumal  motion  is  mentioned  in  Dr.  Williams'  History  of  Vermont. 

S8- 


SO  APPENDIX. 


lands,  filled  with  ledges,  than  in  level,  feasible  laneS  .. 
where  there  are  no  ledges.  As  attractions  are  out  of  sight,  they 
inuat  be  searched  out,  as  before  directed  in  this  work,  by  local 
experiment.  They  often  amount  to  a  quarter,  a  half,  and  some- 
times to  a  whole  degree  or  more.  The  writer  of  this  has  known 
a  difference  of  more  than  five  degrees  within  a  distance  of  forty 
rods. 

When  an  old  line  is  to  be  renewed  where  the  bounds  are  lost, 
the  circumstances  attending  the  case  must  govern.  These  may 
be  various,  such  as  giving  the  lots  on  each  side  of  the  line  and 
contiguous  thereto,  their  full  width  or  quantity,  or  by  dividing 
the  overplus  or  the  wantage,  as  the  case  may  happen.  It  would 
be  difficult  to  mention  all  the  circumstances  which  may  govern, 
or  which  may  serve  as  evidence  in  such  cases. 

After  all,  the  Magnetic  Needle  is  the  best  guide  that  has  yet 
been  discovered,  and  it  cannot  be  dispensed  with  in  land  survey 
ing  ;  but  the  surveyor  who  is  best  acquainted  with  it,  will  make 
as  little  use  of  it  as  he  can.  In  small  surveys,  where  one  angle 
may  be  seen  from  another,  the  quantity  of  each  angle  may  be 
taken  by  an  instrument  constructed  for  that  purpose,  without 
the  use  of  the  Magnetic  Needle  ;  and  the  sides  may  be  measured, 
and  one  side,  no  matter  which,  may  be  made  a  meridian,  and 
from  that  meridian  courses  may  be  calculated  for  the  other  sides, 
and  the  survey  may  be  calculated  by  the  rules  of  rectangular 
surveying.  This  method  has  been  recommended  by  theorists. 
and  the  ingenuity  displayed  in  the  invention,  together  with  the 
correctness  of  it,  so  far  as  it  is  practicable,  must  be  acknow- 
ledged ;  but  in  larger  surveys,  it  cannot  be  introduced  to  prac- 
tice, on  account  of  the  obstructions  which  intervene  between 
the  angular  point  and  the  termination  of  two  contiguous  lines 
which  contain  the  angle  :  in  such  cases,  the  danger  in  taking  the 
quantity  of  an  angle  will  be  greater  than  that  of  the  JMagnetif 
Needle. 

If  in  every  town  in  the  state,  a  meridian  line  was  established  by 
the  motion  of  the  heavenly  bodies,  and  such  meridians  were 
perpetuated  by  durable  monuments,  whenever  a  survey  was  to 
be  taken  in  the  vicinity  of  a  meridian,  a  surveyor  might  set  his 
compass  on  it  and  note  the  variation  found,  and  that  variation 
should  be  inserted  in  the  deed  or  in  whatever  writing  or  instru- 
ment by  which  the  land  is  conveyed  and  made  a  record  ;  thU 
would  assist  a  surveyor  nt  any  future  period  in  retracing  those 
lines,  by  setting  his  compass  on  the  same  meridian  and  allowing 
the  same  variation  that  was  allowed  when  the  survey  was  made, 
'.\\n$  would  tend  greatly  to  the  security  of  landed  property,  and 


APPENDIX.  §7 

perhaps  would  be  the  best  remedy  for  the  variation  o  f  the  Mag- 
netic Needle,  and  for  the  difference  between  two  compasses 
which  differ,  that  can  be  invented. 


On  Practical  Surveying. 

It  would  be  no  easy  matter  to  describe  all  the  different  me 
thods  which  may  be  taken  in  different  cases,  in  taking  the  field- 
work  of  a  survey.     Only  one  case  will  be  given  here,  which  is 
represented  by  the  following  figure.     See  Fig.  1. 

I. 

The  survey  was  begun 
at  the  corner  numbered 
1.  The  corner  numbered 
2  was  in  a  pond.  The 
course  and  distance  were 
taken  from  1  to  »n,  then 
from  in  ion.  The  angle 
at  2  was  a  right  one,  of 
co-urse  there  was  a  right 
angled  triangle,  wherein 
the  angles  and  hypothe- 
nuse  were  given,  to  find 
the  sides  w2  and  2n. 
From  n  to  3,  the  course 
and  distance  were  taken 
on  the  line.  The  next 
line  ran  through  a  thicket  in  a  swamp,  where  nothing  could  be 
done  correctly.  Courses  and  distances  were  taken  from  3  to  s. 
thence  to  zt  thence  to  4,  and  the  course  and  distance  of  the  liae 
3 — 4  were  calculated  by  a  traverse  from  those  courses  and  dis- 
tances. At  the  angle  5,  a  tree  stood  on  a  high  bluff  of  ledges, 
inaccessible  on  either  line  terminating  at  that  point.  The 
course  from  4  to  5  was  taken  at  4.  Next,  the  course  and  dis- 
tance were  taken  from  4  to  a,  and  from  a  the  course  was  taken 
to  5.  Next,  the  course  and  distance  were  taken  from  a  to  6, 
and  from  6  the  course  was  taken  to  5.  Two  oblique  triangles, 
with  the  angles  and  one  side  in  each,  were  given  to  find  the  sides 
4 — 5  and  5 — 6.  The  closing  line  ran  through  thick  bushes  and 
water,  and  the  course  and  distance  were  taken  on  the  dotted 


$8  APPENDJX, 

line  to  the  line  1 — 2,  at  a  point  twenty  rods  from  1 .     The  course 
and  distance  of  6 — 1  were  calculated  accordingly. 

Whenever  a  line  runs  through  or  over  a  place  where  it  is 
difficult  to  take  either  course  or  distance  correctly,  if,  by  taking 
a  traverse  around  at  a  little  distance,  the  surveyor  can  have 
level,  clear  land,  and  then  calculates  his  course  afid  distance  by 
the  traverse,  he  will  he  more  likely  to  ascertain  the  true  course 
and  distance  than  by  continuing  OB  the  line. 


Directions  for  running  Lines. 

Many  people  suppose  that  a  surveyor  at  the  beginning  of  a 
line,  by  intuition  or  by  some  magic  art,  can  set  his  compass  di- 
rectly to  the  terminating  point,  whatever  obstructions  may  in- 
tervene, and  that  he  needs  no  assistants  ;  but  this  is  a  mistaken 
idea.  In  running  a  line  of  considerable  length,  a  surveyor 
should  have  two  assistants  to  carry  the  chain,  and  two  to  carry 
tlags,  in  whose  ability  and  correctness  he  can  confide,  and  a  fifth 
to  use  on  axe.  If  the  surveyor  is  not  furnished  with  such  a  set 
of  assistants,  his  employer  need  not  place  too  much  confidence 
in  his  work.  The  flag  staves  should  be  as  much  as  two  and 
a  half  inches  in  diameter,  or  what  would  be  better,  two  stripes 
of  a  board  of  that  width  and  seven  or  eight  feet  in  length.  If 
they  are  not  so  wide,  they  cannot  be  seen  through  the  sights  of 
the  compass,  at  any  great  distance.  On  one  end  of  each  staff, 
a  red  flag  of  a  yard  in  length  should  be  wound  tight,  and  not  left 
to  hang  loose  and  flutter  in  the  wind.  Red  will  be  seen  quicker 
through  bushes  than  any  other  colour,  and  the  brighter  the  co- 
lour the  better.  Being  thus  manned  and  equipped,  at  the  be- 
ginning of  the  line,  he  must  set  his  compass  as  near  the  true 
line  as  he  can,  or,  what  would  be  better,  he  may  set  up  one  of 
ilie  flags  at  the  place  of  beginning,  and  go  forward  as  far  as  he 
can  have  a  fair  view  of  the  back  flag,  there  set  his  compass  on 
his  random  line,  and  send  the  other  assistant  a&  far  forward  as 
he  can  conveniently  see  the  flag.  When  each  flag  is  clearly 
seen  through  the  sights  of  the  compass,  the  back 'flag  niust.  he 
brought  up  and  placed  where  the  compass  stood.  In  this  maiir 
ner,  he  must  proceed  on  his  random  line,  taking  care  each  time 
he  sets  his  compass  to  turn  the  sights  to  the  back  flag.  Great 
care  must  be  taken  to  keep  these  flags  perpendicular ;  also,  the 
surveyor  must  keep  the  staff  and  the  sights  of  his  compass  per- 
pendicular, A  little  leaning  of  the  flags,  or  turning  the  sight? 


APPENDIX.  8& 

of  the  compass  from  a  perpendicular,  will  make  a  crooked  line. 
In  looking  through  the  sights  of  the  compass  to  the  flags,  the 
surveyor  must  look  as  near  the  ground  as  he  can,  and,  when 
practicable,  the  flag  should  be  turned  down,  on  account  of  the 
danger  of  being  leaned  when  kept  up. 

All  obstructions,  such  ns  bushes,  brush,  &c.  must  be  cleared 
away.  The  random  line  must  be  measured,  and  at  convenient 
distances,  perhaps  at  every  twenty  rods,  stakes  must  be  set  di- 
rectly in  it.  Every  stake  must  be  numbered,  that  no  mistake 
may  be  made  in  calculating,  to  set  them  in  the  true  line.  If,  in 
the  course  of  the  random  line,  the  Magnetic  Needle  does  not 
traverse  as  at  first,  or  traverse  alike  at  different  places,  no  re- 
gard must  be  paid  to  it — the  two  flags  must  direct  the  course  j 
neither  should  the  surveyor  be  turned  aside  or  terrified  by  the  cry 
of  either  of  the  parties,  You  are  wrong,  Yon  are  wrong, (for  he  will 
most  certainly  hear  it,)  but  he  must  continue  hi«  random  line, 
until  turning  at  right  angles  either  to  the  right  or  to  the  left,  as 
the  case  may  be,  he  will  exactly  strike  the  bound,  or  the 'point 
where  a  bound  is  to  be  erected  ;  there  he  may  stop,  and  mea- 
sure the  distance  from  the  termination  of  it  to  the  bound.  Then,, 
having  the  length  of  the  random  line  and  the  distance  to  the 
true  bound,  he  has  the  less  of  a  right  angled  triangle,  the  hy- 
pothenuse  will  be  the  length  of  the  true  line ;  also,  the  angle 
contained  between  the  true  and  the  random  line  must  be  added 
to  or  subtracted  from  the  course  of  the  random  line,  (as  the 
case  may  happen,)  which  will  give  the  course  of  the  true  line. 
Suppose  the  whole  length  of  the  random  line  is  200  rods,  and 
the  distance  from  the  termination  of  it  to  the  bound  is  90  links, 
the  calculation  for  setting  the  stakes  on  the  true  line  may  be 
made  thus  : — As  the  whole  distance  is  to  90  links,  so  is  180,  or 
any  other  20  rods  stake,  to. the  distance  that  such  stake  is  to  be 
moved.  The  answer  is,  the  first  stake  is  to  be  moved  9  links, 
the  second  18  links,  and  so  adding  9  links  at  each  stake  until  the 
whole  are  moved  at  right  angles  from  the  random  on  the  true 
line.  Most  of  the  crooked  lines  and  consequent  disputes  and 
law-suits  between  farmers  have  arisen  for  the  want  of  this  care 
and  attention. 

When  a  long  line  -is  to  be  run  over  a  number  of  ridges  and 
through  intervening  valleys,  it  should  first  be  run  and  established 
from  one  ridge  to  another,  and  the  intermediate  spaces  in  the 
valleys  may  be  taken  afterward.  By  taking  long  sights  there 
will  be  less  danger  of  turning  from  a  straight  line.  In  all  cases, 
the  forward  flag  should  be  carried  as  far  as  it  can  be  distinctly 
unless  it  is  at  the  termination  of  a  line. 


m  APPENDIX, 


..  .  -       ..  ,    ,.,..         .. 

On  keeping  up  Bounds. 

As  the  Magnetic  Needle  cannot  be  relied  on  in  renewing  lost 
boundaries,  it  is  of  the  first  importance  that  good,  substantial 
bounds  be  made  and  kept  up.  In  divisions  or  distributions  of 
lands,  every  surveyor  ought  to  see  that  such  bounds  are  erected. 
It  is  his  business  to  see  them  made,  and  such  bounds  ought  to  be 
described  in  deeds,  or  in  the  instruments  by  which  the  lands  are 
Conveyed,  and  to  be  made  a  part  of  the  record.  By  'proper 
care  and  attention  to  this  part  of  the  business,  almost  an  endless 
train  of  disputes  may  be  prevented.  Highways  are  attended 
with  more  difficulties  of  this  kind  than  the  location  of  any  other 
divisions  of  real  estate.  In  laying  highways,  it  is  the  custom 
to  lay  the  centre  lines,  and  order  them  to  be  of  a  certain  width. 
In  taking  surveys  of  roads,  stakes  are  usually  set  at  the  angles. 
When  the  roads  are  made,  all  these  stakes  are  lost,  and  the  tra- 
velling path  is  often  built  on  one  side  of  the  centre  ;  but  the 
bounds  are  lost,  and  after  a  few  years  have  elapsed,  it  is  utterly 
impossible  to  tell  where  the  road  was  laid. 

Surveyors  who  are  employed  on  such  business  ought  to  de- 
scribe the  angles,  or  as  many  as  is  practicable,  in  such  a  manner 
that  the  road  may  afterward  be  found. 

The  following  Survey  of  a  Road  may  serve  as  an  Example. 

Beginning  at  a  point  on  the  centre  of  an  old  road,  (here  de- 
scribe what  road,)  14  rods  westerly  of  the  range  of  the  west 
end  of  J.  T.'s  house,  thence  running  S.  17°  E.  84  rods  10  links 
to  a  point  bearing  West,  54  links  from  the  S.  W.  corner  of  ti 
large  rock  ;  thence,  S.  5°  E.  77^  rods,  to  a  point  77  links  east 
of  the  centre  of  a  large  white-oak  free  ;  thence,  S.  7°  30'  W. 
C7  rods  20  links,  to  a  point  bearing  West  7  rods  10  links,  from 
a  perpendicular  crevice  in  a  rock. 

Enough  of  the  survey  is  given  to  serve  as  an  example. 

DIRECTIONS    FOR   USING  THE  COMPASS,  AND  CONCERNING  ATTRAC- 
TIONS OF   THE  KE.ED.LE.   ,, 

In  all  cases  the  surveyor  ought  to  set  his  compass  at  least 
tyvice  on  each  line,  even  if  he  has  a  fair  view  of  the  whole 
length  of  it. 

When  there  are  local  attractions,  and  no  two  places  are 
found  on  the  same  line  where  the  compass  has  the  same  tra.- 


APPENDIX.  Oi 

verse,  the  surveyor  should  take  a  medium  and  enter  in  his  field 
book,  noting  such  courses,  as  he  may  still  have  occasion  tocoi1- 
rect  them  in  his  calculations.  If  in  such  cases  he  is  at  a  loss 
what  course  to  enter  in  his  field  book,  and  suspects  that  some 
minutes  may  be  added  to,  or  subtracted  from  the  course  he 
enters  in  his  book,  let  him  prefix  to  such  courses  the  sign  of 
addition  or  subtraction  as  the  case  may  be,  which  will  often 
assist  him  in  balancing  his  surveys. 

CONCERNING  DRAWING  A  MAP  OF  A  FIELD. 

When  a  map  is  to  be  made  of  a  multangular  piece  of  land, 
whether  a  calculation  or  division  is  to  be  made  from  it,  the  sur- 
veyor should  measure  across  the  lot  in  some  central  place  at 
least  once,  and  in  more  places  if  convenient  and  the  case  may 
require  it.  By  cross  measures,  the  map  will  be  made  more 
correct.  The  surveyor  should  not  be  afraid  of  wearing  his 
chain  by  measuring  too  much.  When  a  survey  is  to  be  calcu- 
lated by  plotting,  it  should  not  be  laid  on  a  scale  less  than  tea 

rotls  to  an  inch. 

'•     . 

REMARKS  ON  BALANCING  A  SURVEY. 

In  every  survey  which  is  accurate,  the  sum  of  the  Northing's 
will  equal  that  of  the  Southings,  and  the  Eastings  will  equal 
the  Westings  ;  but  this  is  not  always  an  infallible  proof  that 
the  survey  is  accurate,  for  two  errors  may  be  committed,  one 
exactly  to  balance  the  other,  which  no  rule  will  detect ;  but 
such  cases  do  not  often  occur.  In  a  survey  of  one  hundred 
acres,  whatever  may  be  the  number  of  the  angles,  the  differ- 
e,nce  between  the  two  columns  of  Latitude  and  those  of  Depar- 
ture3  ought  not  to  exceed  a  rod  for  each,  but  to  come  within 
these  limits  if  possible. 

If  in  such  a  survey  either  of  the  differences  should  exceed  a 
rod,  where  the  land  is  valuable  and  easily  surveyed,  it  would 
be  better  to  take  a  re-survey,  or  so  far  as  to  detect  the  error. 

Some  authors  have  given  rules  for  balancing  surveys,  which 
are  indiscriminately  applied  to  every  line  in  the  survey,  which 
presupposes  that  a  proportional  error  must  have  been  commit- 
ted on  each  and  all,  both  in  courses  and  distances,  when  in  al- 
most every  survey,  a  part  of  the  lines  are  on  land  so  level  and 
so  clear  from  obstructions  of  any  kind,  that  if  the  surveyor  and 
chaiimien  attend  to  their  b«sine.ss,  they  will  not  be  likely  to 


92  APPENDIX. 

commit  much  error  on  them ;  while  other  lines,  on  other  parts 
of  the  same  survey,  are  attended  with  so  many  difficulties, 
that  when  they  have  done  their  best,  it  will  scarcely  be  possible 
for  them  to  avoid  some  error,  and  the  surveyor  who  takes  the 
survey  will  best  judge  on  what  lines  the  errors  were  committed, 
and  whether  they  are  hi  the  courses  or  in  the  distances.  In  all 
cases  the  corrections  should  be  made  on  the  lines  containing 
the  errors.  When  the  errors  are  in  the  courses  they  should 
be  corrected,  and  when  the  errors  are  in  the  distances,  the  cor- 
rection should  be  in  them  :  or  the  corrections  may  be  in  both 
courses  and  distances  as  the  surveyor  may  judge  proper. 

When  a  course  is  northwesterly  and  southeasterly,  or  north- 
easterly and  southwesterly,  if  the  correction  of  it  increases  the 
latitude  and  diminishes  the  departure,  or  if  it  diminishes  the 
latitude  and  increases  the  departure,  so  as  to  bring  the  differ- 
ences to  an  even  balance,  it  is  good  evidence  that  the  course 
contains  some  error. 

f    f>*  *1  "(SV 'ifc    r  f:>.  i  W       ..fix".  -71  tj:.;*  3.j:ii?r*.]')Kl  rvrf-  fli-Gft  • 

On  Rectangular  Surveying. 

Rectangular  Surveying  is  a  name  given  to  the  method  here 
treated  of,  by  the  late  Governor'Treadwell. 

A  more  appropriate  name  could  not  have  been  given ;  for 
the  whole  survey  is  reduced  to  right  lined  figures,  such  as 
triangles,  trapezia,  squares,  and  parallelograms.  It  is  simply 
multiplying  the  latitudes  by  the  longitudes  from  a  meridian 
from  which  the  survey  is  calculated. 

The  calculations  are  made  from  a  meridian,  drawn,  either  at 
the  eastern  or  at  the  western  extremity  of  the  map.  All  the 
spaces  lying  between  the  field  and  the  meridian  from  which  the 
survey  is  calculated,  and  between  the  parallels  of  latitude  of 
the  northern  and  southern  extremities  of  it,  are  included  in  the 
calculation.  Parallels  of  latitude  are  drawn  from  each  angle 
to  the  meridian,  which  are  called  meridian  distances. 

In  forming  the  column  of  meridian  distances,  when  the  meri- 
dian is  drawn  at  the  eastern  extremity,  the  westings  are  added 
and  the  eastings  are  subtracted.  When  the  meridian  is  drawn 
at  the  western  extremity,  the  eastings  are  added,  and  the  west- 
ings are  subtracted. 

The  meridian  distances  proceeding  from  each  end  of  a  line, 
are  added  together,  to  form  the  column  of  double  mean  dis- 
tances, which  the  compiler  of  the  foregoing  work  has  called 
second  departure  column. 

The  whole  is  illustrated  by  the  following  ^ure.     See  Fig.  2: 


APPENDIX. 


Directions  for  calculating  meridian  distances  by  several  methods ; 
also,  for  plotting  a  survey,  from  the  several  latitudes  and  meridian 
distances,  without  the  use  of  the  protractor,  or  the  line  ef  chords. 


8 


wlS 

yu 


:* 


21 


8 


E 


8 


8 


-' 


94 


APPENDIX. 


Fig.*. 


80-07 


Meridian  Dis- 
tances,  and  Double 
Mean  Distances, 

•  +*• :Vw  t  7f# 

are  more  proper 
terms  or  names  for 
the  eighth  and  ninth  ?/ 
columns,  than  first 
Departure,  and  se- 
cond Departure. 

The  meaning  of  a 
the  term  Meridian 
Distance  is  the  dis-    s 
tance   made   from 
any  Meridian.      It 
is  not  very  essen- 
tial by  what  names 
the    columns    are 
called,    as  names 
have  no  effect  on    ± 
the  final  result. 


This  survey  is  calculated  from  the  meridian  of  the  firlt  sta- 
tion. 

To  form  the  first  column,  marked  at  the  top,  Merid.  Dist., 
set  the  easting  16.90  against  the  first  station  into  the  column, 
which  is  the  meridian  distance  of  2,  or  the  distance  from  2  to  1  ; 
to  this  number  add  the  next  easting,  and  they  make  22.11, 
the  meridian  distance  of  3  ;  to  this  number  add  the  next  east- 
ing, and  they  make  80.07,  the  meridian  distance  of  4  ;  from 
this  number,  subtract  the  first  westing,  and  73.82  remains,  the 
meridian  distance  of  5  ;  from  this  number,  subtract  the  nex^t 
westing,  and  70.33  remains,  the  meridian  distance  of  6,  or  the 
westing  of  the  closing  line.  Subtract  the  last  westing,  and 
00.00  remains.  This  is  on  the  principle  of  going  around  a 
circle.  Next,  form  the  column  of  double  mean  distances  by 
adding  two  opposite  sides  of  the  different  figures.  Set  the  first 
Merid.  Dist.  into  the  column.  To  the  first  meridian  distance, 
add  the  second,  and  they  make  39.01,  the  double  of  the  figure 
23ns.  To  the  second,  add  the- .hird,  and  they  make  102.18, 
the  double  of  the  figure  34nw.  To, the  third,  add  the  fourth, 
and  they  make  153.89,  the  double  of  the  figure  45am.  To  the 
fourth,  add  the  fifth,  and  they  make  144.15,  the  double  of  the 
figure  56oz.  To  the  fifth,  add  the  sixth,  and  they  make  70.33. 


APPENDIX.  95 

The  second  column,  marked  at  the  top,  Merid.  Dist.,  is 
commonly  called  the  Pennsylvania  method.  Only  one  column 
is  used  in  finding  the  meridian  distances,  but  the  operation 
and  final  results  are  the  same  as  that  when  two  columns  are 
used.  This  method  is  not  so  easily  explained  to  the  learner, 
but  is  preferable  in  practice  only  because  an  error  may  be  com- 
mitted in  forming  the  column  of  double  mean  distances  which 
may  not  be  discovered,  but  in  this  method  an,  error  cannot  be 
committed  without  being  detected. 

To  form  this  column,  set  the  first  easting  16.90  in  the  upper 
place,  and  add  it  to  itself  and  they  make  33.80  ;  to  this  number, 
add  the  next  easting,  and  they  make  39.01  ;  add  the  same 
easting  again,  and  they  make  44.22  ;  to  this  number,  add  the  last 
easting,  and  they  make  102.18  ;  add  the  same  easting  again,  and 
they  make  160.14  ;  from  this  number,  subtract  the  first  west- 
ing, and  153.89  remains  ;  subtract  the  same  westing  agciin, 
and  147.64  remains ;  from  this  number,  subtract  the  second 
westing,  and  144. 15  remains  ;  subtract  the  same  westing  again, 
and  140.66  remains  ;  from  this  number  subtract  the  last  westing, 
and  70.33  remains  ;  subtract  the  same  westing  again,  and  00.00 
remains. 

The  upper  numbers  in  this  column  are  the  same  as  the  double 
mean  distances  which  stand  against  them. 

For  the  remainder  of  the  process  in  finding  the  areas,  pro- 
ceed as  before  taught  in  this  work. 

The  north  area  against  the  first  station  is  the  double  of  the 
triangle  12* ;  that  against  the  second,  is  the  double  of  the  figure 
23ns  ;  that  against  the  third,  is  the  double  of  the  figure  34ww  ; 
the  south  area  against  the  fourth  station,  is  the  double  of  the 
figure  45am  ;  that  against  the  fifth,  is  the  double  of  the  figure 
56*a  ;  that  against  the  sixth,  is  the  double  of  the  triangle  61z. 

The  three  north  areas  all  lie  without  the  field,  and  are  bound- 
ed north  on  the  line  w4.  The  three  south  areas  contain  all 
within,  and  all  without  the  field,  which  is  included  in  the  calcu- 
lation. It  is  obvious  then  that  when  the  less  is  subtracted  from 
the  greater,  the  contents  of  the  field  will  remain. 

Another  column  may  be  formed  as  the  eleventh  in  this  ex- 
ample, which,  for  distinction,  is  here  called  half  departure.  It 
contains  half  the  sum  of  the  numbers  in  the  double  mean 
column.  These  numbers  when  multiplied  by  their  respective 
northings  or  southings,  give  the  simple  areas  of  the  different 
figures.  This  method  is  preferable  in  practice,  as  the  multi- 
plications are  greatly  diminished.  When  the  last  decimal  in 
the  double  mean  distance  is  an  odd  number,  a  unit  may  be  taken 


96  APPENDIX. 

off,  and  take  half  the  remainder  rather  than  annex  another  de- 
cimal. Perhaps  this  would  not  make  the  difference  of  a  rod  in 
a  survey  of  one  hundred  acres,  or  the  odd  numbers  in  the  last 
place  of  decimals  may  be  balanced  by  sometimes  adding  a  unit. 
If  the  numbers  are  diminished  a  trifle,  it  may  be  remarked, 
that,  on  account  of  the  uneven  surfaces,  there  is  danger  of 
making  the  distances  too  much  rather  than  falling  short  of  the 
true  measure. 

To  plot  the  foregoing  Field  from  Hie  several  Latitudes  and 
Meridian  Distances,  without  the  use  oj  the  protractor,  or  the  line 
of  Chords. 

First,  set  the  northing  of  the  first  line  from  1  to  s ;  set  the 
northing  of  the  second  line  from  s  to  n ;  set  the  northing  of  the 
third  line  from  n  to  m  ;  set  the  southing  bi  the  fourth  line  from 
m  to  a  ;  set  the  southing  of  the  fifth  line  from  a  to  s ;  next, 
from  these  points,  draw  parallels  of  latitude  perpendicular  to 
the  meridian ;  then,  on  these  parallels  of  latitude,  set  the  me- 
ridian distances  of  the  several  stations  from  sto  2, 16.90  ;  from 
n  to  3,  22.11 ;  from  m  to  4,  80.07 ;  from  a  to  5,  73.82  ;  from  z 
to  6,  70.33.  From  one  of  these  last  points  to  another,  draw 
the  boundary  lines  of  the  field,  and  if  the  plan  does  not  per- 
fectly close,  it  is  because  some  error  was  committed  in  the 
process,  or  the  scale  was  incorrect.  In  practical  surveying,  it  is 
next  to  an  impossibility  in  any  case,  to  work  so  accurately  that 
the  survey  will  exactly  close  without  some  correction.  The 
difference  between  the  two  columns  of  latitude,  and  the  two 
columns  of  departure,  are  the  legs  of  a  right  angled  triangle,, 
the  hypothenuse  of  which  will  be  the  distance  which  the  sur- 
vey will  fail  of  closing. 

These  differences,  as  before  taught  in  this  work,  must  be 
balanced,  and  the  column  of  meridian  distances  must  be  formed 
by  the  numbers  as  balanced.  When  the  survey  is  balanced, 
and  this  method  of  plotting  is  taken,  the  parallels  of  latitude 
must  be  laid  down  according  to  the  balancing,  and  the  map 
will  perfectly  close. 

When  the  courses  and  distances  are  corrected  according  to 
the  balancing,  they  will  form  a  survey  which  will  contain  no 
error. 

N.  B.  Great  care  must  be  taken  to  keep  the  latitudes  paral- 
lel and  perpendicular  to  the  meridian.  The  better  to  effect 
this,  a  meridian  line  may  be  laid  on  each  side  of  a  sheetj  or  a 
half  sheet  of  paper,  as  the  occasion  may  require. 


APPENDIX. 


97 


The  follomng  survey  is  calculated  from  a  m&idim  running 
tfa'ough  the  map  :  of  course,  part  of  the  meridian  distances  are 
east,  and  part  are  west.  See  Fig.  3. 

Fig.  3. 


o.    Courses   Rods    N. 

S. 

E. 

W. 

1  N60°00'E. 

i 

20.00  10.00 

17.32 

17.32 
34.64 

E. 
E. 

173.20 

2  S.30  OOE. 

i 

40.00 

| 

34.64 

20.00 

54.64  E, 
74.64E. 

1892.73 

3  S.70  OOW. 

70.00 

40.00  34.64 

23.94 

65.78 
20.00 

8.86  E. 
56.92W 

212.10 

1 
4  N.30  OOW. 

i 

76.92W 
96.92W 

2664.50 

J 
5N.74  OOE. 

50.42  13.94 

48.46 

48.46  W 
00.00| 

675.53 

173.20  5444.86 
173.20 

2)5271. 
-  A.  Q.  R. 

160)2635(16    i    35 
160 

1035 
960 


9&  APPENDIX. 

The  column  of  meridian  distances  in  this  example  is  formed 
by  adding  twice,  and  subtracting  twice  against  each  station,  as 
in  the  Pennsylvania  method.  Set  the  first  easting  in  the  upper 
place,  which  is  the  distance  from  a  to  2,  being  east  meridian 
distance  ;  add  it  to  itself,  and  it  makes  34.64  ;  to  this  number, 
add  the  next  easting,  and  they  make  54.64,  east  meridian  dis- 
tance from  a  to  w ;  add  the  same  easting  again,  and  they  make 
74.64 ;  from  this  number,  subtract  the  first  westing,  and  there 
remains  8.86  east  meridian  distance  from  t  to  s.  As  the  first 
westing  cannot  be  subtracted  again,  the  last  east  meridian  dis- 
tance, 8.86,  must  be  subtracted  from  the  first  westing ;  this 
Crosses  the  meridian,  and  gives  56.92  west  meridian  distance 
in  the  lower  place.  Having  crossed  the  meridian,  the  westings 
must  now  be  added,  and  the  eastings  subtracted. 

To  the  56.92  in  the  lower  place,  add  the  last  westing,  and 
they  make  76.92  west  meridian  distance  from  r  to  « ;  add  the 
same  westing  again,  and  they  make  96.92 ;  from  this  number, 
subtract  the  easting  of  the  closing  line,  and  there  remains 
48.46  west  meridian  distance,  from  v  to  1,  or  the  easting  of  the 
closing  line ;  subtract  again,  and  00.00  remains.  Having  com- 
pleted the  column  of  meridian  distances,  next  multiply  the 
upper  number  against  each  station,  by  its  northing  or  southing, 
and  set  the  products  on  the  east  side  of  the  meridian,  in  their 
respective  columns  of  north  or  south  areas ;  but  on  the  west 
side  of  the  meridian,  the  order  is  reversed  ;  the  north  products 
are  setinfhe  column  of  south  areas,  and  the  south  products  are 
set  in  the  column  of  north  areas.  The  north  area  against  the 
first  station,  is  the  figure  2zla ;  the  south  area  against  the 
second  station,  is  the  figure  mnia  ;  the  south  area  against  the 
third  station,  is  the  figure  sxie ;  the  south  area  against  the  fourth 
station,  is  the  figure  uioer,  made  by  the  northing  of  the  fourth 
line  ;  the  south  area  against  the  last  station,  is  the  figure  vbrl. 

The  foregoing  columns  of  meridian  distances  might  have 
been  commenced,  by  setting  the  first  easting  in  the  lower  place, 
nntl  the  additions  and  subtractions,  made  as  before  directed, 
and  the  last  subtraction  would  end  in  00.00  at  the  upper  place, 
against  the  first  station.  In  this  case,  as  there  would  be  no 
upper  number  against  the  first  station,  there  would  be  no 
product  in  either  column  of  areas  against  it.  The  east  meri- 
dian distance  against  the  second  station  would  extend  no  further 
east  than  the  third  station,  and  the  meridian  distance  against 
the  third  station,  would  hp  on  the  west  side  of  the  meridian ; 
;md  the  meridian  distances,  against  the  fourth  and  fifth  stations, 
would  extendas  much  farther  west,  as  the  easting  of  the  first  line 


APPENDIX.  $P 

The  products  against  the  second,  fourth,  and  fifth  stations, 
would  be  set  in  the  column  of  south  areas,  and  thaj  against  the 
third  station,  on  account  of  its  heing  on  the  west  side  of  the 
meridian,  would  be  placed  in  the  column  of  north  areas,  and 
would  be  subtracted  from  the  footing  of  the  south  areas. 

When  a  survey  is  calculated  from  a  meridian  running  through 
the  map,  it  is  always  best  to  set  the  first  departure  in  the  lower 
place,  as  it  saves  one  multiplication. 


On  Distributing  Estates. 

A  farm  is  to  be  distributed  among  a  number  of  heirs.  A 
survey  is  made,  and  the  difference  between  the  columns  of  lati- 
tude, and  between  those  of  departure,  are  two  rods  for  each. 
The  survey  is  balanced,  and  calculated  arithmetically,  and  is 
found  to  contain  two  hundred  acres.  The  surveyor  next  draws 
his  map,  by  which  the  divisions  are  to  be  made,  according  to 
the  courses  and  distances.  The  plan  does  not  close  by  nearly 
two  rods  and  three-quarters.  He  next  corrects  the  lines,  and 
makes  the  map  close  as  well  as  he  can  ;  and  when  the  divisions 
are  made,  they  may  not  agree  with  the  first  calculation  by  two 
or  three  acres,  or  more.  Should  the  map  be  drawn  as  before 
directed,  by  the  meridian  distances  and  the  latitudes  as  balan- 
ced, it  would  close,  and  would  be  in  exact  conformity  to  the 
calculation  made  arithmetically.  If  the  divisions  are  made 
arithmetically,  without  the  use  of  the  scale  and  ^dividers,  the 
calculations  must  be  made  according  to  the  balancing,  or  the 
divisions  will  not  agree  with  the  first  calculation. 

It  will  be  acknowledged  by  every  experienced  surveyor,  that 
It  is  a  difficult  matter  to  make  the  amount  of  a  considerable 
number  of  divisions  agree  with  the  whole,  when  calculated  by 
itself. 

It  is  the  common  practice  in  distributions,  to  make  the  di- 
visions with  scale  and  dividers ;  this  method  will  answer  very 
well  provided  the  map  is  drawn  on  a  large  scale. 

The  following  is  a  useful  rule  in  dividing  lands,  when  any 
quantity  is  to  be  added  to,  or  taken  from,  a  division  in  the  form 
of  a  triangle. 

Having  the  area,  the  contained  angle,  and  one  side  of  a  tri~ 
Angle  given,  to  find  the  adjoining  side,  including  the  angle, 


100  APPENDIX. 


_ 
RULE. 

To  the  sine  of  the  given  angle,  or  its  supplement  if  obtuse, 
add  the  logarithm  of  the  given  side  ;  subtract  radius  from  this 
sum,  and  subtract  the  remainder  from  the  logarithm  of  the 
double  area,  the  last  remainder  will  be  the  logarithm  of  the 
side  required. 

In  taking  a  survey,  go  around  with  the  sun,  not  that  you  can 
work  more  correctly,  or  that  it  will  have  any  effect  in  calcula- 
ting, but  when  you  put  your  courses  and  distances  on  your  map 
they  will  follow  around  with  the  lines,  from  the  left  to  the 
right. 

Wherever  you  begin,  set  yotir  compass  on  the  angle  and  cause 
n.  stake  or  a  flag-staff  to  be  erected  at  the.  next.  When  your 
line  runs  over  a  hill,  cause  a  *take  to  be  erected  at  each  end  of 
it,  and  take  your  station  on  the  top  of  the  hill,  directly  between 
them.  If  bushes  obstruct  the  sight,  make  an  offset,  or  set  your 
compass  a  little  distance  from  the  line,  from  whence  you  may 
see  the  back  flag,  and  cause  the  forward  flag  or  stake  to  be  set 
against  the  bound  in  a  direction  with  the  compass  and  the  back 
flag.  When  the  line  is  measured,  measure  the  distance  from 
the  flag  to  the  bound,  and  calculate  your  true  course  by  Trigo- 
nometry. If  your  next  line  is  of  such  a  distance  that  you  can- 
not see  through  the  whole  length  of  it,  run  as  near  the  true 
line  as  you  can,  and  if  you  do  not  exactly  strike  the  bound, 
measure  the  distance  from  the  termination  of  your  random  line, 
and  calculate  your  course  as  before  directed,  or  if  you  can  dis- 
cover a  tree  standing  near  the  termination  of  your  line,  take 
the  course  and  distance  to  that,  thence  to  the  bound,  and  calcu- 
late your  true  course  and  distance. 

By  practice  and  experience,  a  method  for  taking  courses  will 
soon  become  familiar,  in  all  cases.  In  measuring  hills  and  in- 
clined surfaces,  the  horizontal  distances  must  be  taken.  A 
plummet  should  be  suspended  from  the  end  of  the  chain,  when 
it  is  levelled.  Where  hills  are  very  steep,  the  surveyor  should 
assist  the  chainmen,  and  when  the  best  is  done  in  levelling  and 
plumbing  the  chain,  judgment  must  frequently  be  called  into 
exercise.  Even  when  rises  and  descents  are  easy,  there  is 
danger  of  m?king  too  much  measure.  In  such  cases,  chainmea 
often  make  allowances,  but  the  surveyor  would  do  better  to 
keep  them  to  close  measure,  and  from  the  shape  of  the  ground 
judge  himself  what  allowances  ought  to  be  made.  If  he  is  ex- 
perienced in  his  business,  he  will  form  a  more  correct  judgment 


APPENDIX. 

than  inexperienced  chainmen.  Particular  care  must  be  taken 
that  the  chain  is  carried  on  a  straight  line,  and  that  it  is  well 
straightened.  When  a  tally  is  ended,  and  the  hinder  chamman 
brings  up  the  sticks,  they  must  be  counted. 

When  on  counting  the  sticks  it  is  discovered  that  one  is  lost 
the  chainmen  should  not  leave  the  chain  and  go  back  to  find  it, 
but,  from  the  last  mark,  should  measure  back  to  the  point  where 
the  tally  began,  to  see  whether  one  chain  is  lost  from  their  mea- 
sure. Many  blunders  in  this  way  have  been  left  undetected  by 
not  taking  this  care. 

A  careful  accurate  chainman  never  lost  a  stick  or  miscounted 
a  tally.  Young  surveyors  should  practice  much  for  their  own 
instruction,  and  should  make  correct  practice  familiar,  before 
they  offer  their  services.  It  is  as  necessary  that  they  should 
spend  some  time  in  acquiring  a  practical  knowledge,  as  it  is  that 
they  should  spend  any  time  in  acquiring  a  knowledge  of  theory, 

A  young  surveyor  should  bear  in  mind  that  if  he  is  detected 
in  one  error  i»  the  beginning  of  his  practice,  it  will  be  more  to 
his  disadvantage  than  to  be  detected  in  two  when  he  shall  be 
well  established.  If  an  error  is  committed  in  a  survey,  it  is 
not  against  the  surveyor  provided  he  detects  and  corrects  it, 
but  if  he  cannot  detect  and  correct  his  own  errors,  that  is  suffi- 
cient evidence  of  his  deficiency  in  point  of  knowledge  and 
skill. 


Form  of  a  Field  Book. 

Beginning  at  a  murstone  at  the  southwest  corner, 

Rods  Links 

1.  N.  250  00'  E.  40  00     to  a  white-oak  tree, 
2:  N.  10     00  E.  30  00     to  a  heap  of  stones, 

3.  N.  75     00  E.  60  00     to  a  maple  tree, 

4.  S.    10     00  W.  36  00     to  a  pine  tree, 

5.  S.     5     00  W.  40  00     to  a  spruce  tree, 

6.  S.  85     05  W.  70  12     to  the  place  of  beginning. 
When  a  survey  is  calculated  by  chains  and  links,  the  numbers 

are  less  than  when  it  is  calculated  by  rods  and  decimal  parts, 
Every  method  by  which  the  numbers  are  diminished  is  an  im- 
provement. In  a  hilly  country,  the  two-pole  chain  is  prefera- 
ble and  is  more  commonly  used,  because  it  can  be  levelled 
better. 

Hills  are  often  found  so  steep  that  even  the  two-pole  chaia 
cannot  be  levelled* 


APPENDIX. 


MISCELLANEOUS. 

When  a  surrey  is  calculated  by  chains  and  links,  and  the  con- 
tents stand  in  acres  and  decirfial  parts  of  an  acre,  it  may  be  mul- 
tiplied by  the  price  of  an  acre,  and  the  product  will  be  the 
amount. 

EXAMPLE. 

A  piece  of  land,  12  chains  and  25  links  in  length,  and  10 
chains  and  25  links  in  breadth,  is  sold  for  $20  25,  per  acre  ;— 
what  is  the  price  of  it  ? 

Length  12.25 
Breadth  10.25 


Acres  and  decimal  parts  12.55625 
Price  of  an  acre        20.25 

6278125 
2511250 
2511250 


Answer  $254, 26. 40625 

The  writer  of  these  pages  knows  not  who  invented  the  fol- 
lowing rules  for  finding  contained  angles.  For  plainness,  none 
of  the  kind  exceeds  them. 

N   62O  E      1      When  the  first  letters  are  alike,  and  the  two 
N   44    W       '  Iast  are  ""''ke,  ac^  tne  degrees  of  both  courses 

J  together,  which  gives  the  contained  angle. 
S   72°  E       1       When  the  two  first  and  the  two  last  letters  are 
S  25    E        '  alike,  subtract  one    course  from  the  other,  and 
j  the  remainder  will  be  the  contained  angle. 

!When  the  two  first  letters  are  unlike,  and  the 
two  last  alike,  add  both  courses  together,  and  sub- 
tract their  sum  from  180,  the  remainder  will  be 
the  contained  angle. 

"}      When  the  two  first  and  the  two  last  letters  are 
N.  57°  W.    !  unlike,  subtract  one  course  from  the  other,  the 
S.  25    E.     f  remainder  from  180,  and  the  remainder  will  be 
J  the  contained  angle. 

Application  of  the  above  Rules. 
Two  courses  are  given,  viz.  N.  67°  W.  and  N.  28°  E.  to  find 


APPENDIX.  103 

the  angle.— Suppose  yourself  standing  at  the  point  where  these 
courses  meet.  Reverse  the  letters  of  the  first  course,  and  they 
will  stand  thus, 

S.  670  E.  >      The  third  rule  applies  in  this 
N.  28    E.Jcase. 

When  the  quantity  of  any  angle  in  a  survey  is  wanted,  the 
preceding  course  must  be  reversed  ;  then  both  courses  will  run 
from  the  Same  point. 

Converging  of  Meridians. 

The  breadth  of  a  degree  of  longitude  in  any  parallel  of 
latitude  is  to  the  breadth  of  a  degree  upon  the  equator,  as  the 
Co-sine  of  thai  Lat.  is  to  Radius. 

R.  :  60  Miles  :  :  Co-sine  of  the  Lat.  :  the  breadth  of  a  degree 
on  that  Lat. 

As  Radius  -  10.00000 

Is  to  60  Miles,      -  1.77815 

So  is  Co-sine  Lat.  60°       9.69897 


11.47712 

10.00000 

To  30  Miles         -    -        1.47712 


MISCELLANEOUS  QUESTIONS. 

1.  At  a  certain  point  I  took  the  elevation  of  a  tower  3°  15 
— then  measured  toward  the  tower  on  an  angle  of  depression 
7°  333  feet  to  a  level  with  the  base  of  the  tower,  when  I  took 
the  elevation  again  8°. — Required  the  height  of  the  tower  and 
the  distance  from  the  second  place  of  observation  to  the  base  ; 
also  how  much  higher  the  land  was  at  the  place  of  the  first  ob- 
servation than  at  the  second. 

Ans.— Height,  99.6   feet. 

Distance  required,  -       708.6   feet. 

Difference  in  the  height  of  land,  40.58  feet . 

2.  Two  persons  made  observations  on  the  altitude  of  a  me- 
teor, both  being  on  the  same  side  of  it,  and  in  a  vertical  plane 
passing  through  it.     The  distance  of  their  stations  were  200 
rods  apart,  and  at  one  the  angle  of  elevation  was  36°  25',  at 
the  .other  32°  50',  and  at  the  last  the  outer  limb  of  the  meteor 


104  APPENDIX. 

subtended  an  angle  of  2'. — Required  the  distance  from  thfc 
last  place  of  observation,  also  the  height  and  diameter  of  it. 

M.     Q.     R. 

Answer. — The  distance,  5  ..  3  ..  60 
Height,  3  ..  0  ..  70 
Diameter,  1 8  feet  2  inches. 

3.  From  the  top  of  a  steeple  165  feet  high,  the  angle  of  depression  of  the 
nearest  bank  of  a  river  is  11°  15',  that  of  the  opposite  bank  is  6°  15'.    Re- 
quired the  width  of  the  river.  Jlnsw.  41.13  rods. 

4.  What  length  of  cart-tire  will  it  take  to  band  a  wheel  5  feet  in  diameter  ? 

Jlnsw.  15  feet  8  1-2  inches. 

5.  A  gentleman  laid  out  a  garden  in  a  circle,  containing  one  acre,  one 
quarter,  and  one  rod,  with  a  gravelled  walk  on  the  outer  side  of  it  within 
the  circle  which  took  up  twelve  rods  of  ground.    What  is  the  diameter  of 
tine  circle,  and  what  is  the  width  of  the  walk  ? 

Jlnsw.     The  diameter  16  rods— Width  of  the  walk  4  feet. 

6.  Neptune  laid  out  1000  square  miles  of  the  surface  of  the  sea  in  a  circle, 
and  sold  to  Aeolus  all  that  part  of  it  which  lies  without  a  concentric  circle  of 
ane  third  of  the  diameter.     What  is  the  diameter,  and  how  much  was  sold  ? 

Jlnsw.    The  diameter  35.68  mites.     The  quantity  sold  888.92  square  miles. 

7.  A  Farmer  laid  out  an  elliptical  orchard,  the  longest  diameter  of  which 
was  30  rods,  and  the  shortest  was  20  rods,  and  surrounded  the  same  with  a 
wall  two  feet  thick,  within  the  figure.     What  is  the  quantity  within  the  wall., 
and  how  much  is  covered  by  it  ?  A.     Q.    JR. 

Jlnsw.     Within  the  waU  2  ..  3  ..22 

Covered  by  the  wallt         9.3  rods. 

8.  From  a  point  in  an  equilateral  triangle,  I  measured  the  distances  to  each 
corner,  and  found  them  20,  29,  and  30  rods.    Required  the  area  and  the 
length  of  the  sides.*  A.    Q.    R. 

Jlnsw.     The  Area  5  ..  1   ..33 
Length  of  each  side  45  rods. 

9.  Required  the  dimensions  of  a  parallelogram,  containing  one  acre  and 
a,  half,  bounded  by  64  rods  of  fence.  Jlnsw.  12  by  20  rods. 

10.  The  area  of  a  parallelogram  is  five  acres  one  quarter  and  thirty-five 
rods,  and  the  diagonal  is  forty- three  rods.     Required  the  length  of  the  sides. 

Jlnsw.  35  by  25  rods. 

11.  Required  the  dimensions  of  a  parallelogram  containing  twenty-six 
acres  one  quarter  and  twenty- four  rods,  when  the  length  exceeds  the  breadth 
by  fifty-two  rods.  \         Jlnsw.  44  by  96  rods. 

12.  Required  the  dimensions  of  a  parallelogram  containing  250  acres, 
when  the  sides  are  in  the  proportion  of  7  to  3.    Jlnsw.  130.93  by  305  1-2. 

13.  The  state  of  Connecticut  contains  a  little  upwards  of  4828  square 
miles,  or  3,090,000  acres,  including  rivers,  harbours,  creeks,  roads,  &c.  if 
this  quantity  of  land  is  laid  in  a  square,  what  will  be  the  length  of  eaqh 
side?  M.     Q.     R. 

Jlnsw.    69  ..  1  ..  75.11 

JVWe.  In  the  Preface,  it  is  observed  that  the  Traverse  Table  in  this  book 
is  calculated  for  any  distance  up  to  50.  After  the  Preface  was  printed,  it 
was  thought  best  to  extend  that  Table  to  70.  The  table  of  Logarithms  is 
also  much  more  extensive,  than  is  noticed  in  the  Preface. 

*  This  maybe  solved  geometrically. 


MATHEMATICAL  TABLES. 


VIZ: 


I.  A  Table  of  Logarithms  for  Numbers. 

II.  A  Table  of  Logarithmic  or  Artificial  Sines,  Tangents,  and 
Secants. 

III.  A  Traverse  Table,  or  Table  of  Difference  of  Latitude  and 
Departure. 

IV.  A  Table  of  Natural  Sines. 


I.    A  TABLE  OF  LOGARITHMS  FOR  NUMBERS. 

- 

Logarithms  are  Numbers  in  Arithmetical  Progression,  corres- 
ponding to  other  Numbers  in  Geometrical  Proportion. 
As,  0.  1.  2.  3.  4.    Logarithms. 

1.  10.          100.        1000.      10000.  Numbers, 

The  Logarithm  for  any  Number  less  than  10  is  a  certain 
number  of  Decimals  ;  for  any  Number  between  10  and  100, 
it  is  1  with  Decimals  ;  for  any  Number  between  100  and  1000, 
it  is  2  with  Decimals,  &c.  The  whole  Number  in  Logarithms, 
or  the  Number  which  stands  at  the  left  hand  of  the  Decimal 
point,  is  called  the  Index  ;  and  is  always  a  unit  less  than  the 
places  of  figures  in  the  whole  Number  for  which  it  is  the  Lo- 
garithm :  Thus, 

The  Log.  of  6543  is  3.81578 

654.3  2.81578 

65.43          -  1.81578 

6.543       -  0.81578 

The  Log.  of  a  Decimal  Fraction  is  the  same  as  that  of  an 
Integer,  only  the  Index  is  negative,  and  is  distinguished  from  a 
positive  one,  by  placing  a  Point,  or  a  negative  Sign  before  it : 
Thus, 

The  Log.  of  0.6543         is          .9.81578  or  —1.81578. 
0.06543  .8.81578  or  — 2.8T578. 

Note. — In  the  following  Table  the  Index  is  not  prefixed.  It 
may  be  easily  supplied  as  it  is  always  a  unit  less  than  the  number 
of  figures  in  the  corresponding  natural  whole  number. 

1 


2  LOGARITHMS. 

To  find  the  Logarithm  of  any  Number. 

If  the  Number  is  less  than  100,  its  Log.  is  found  in  the  first 
page  of  the  Table,  directly  opposite  thereto  :  Thus,  the  Log. 
of  34  is  1.53148. 

If  the  Number  consists  of  three  figures,  find  it  in  the  first 
column  of  the  following  part  of  the  Table,  opposite  to  which, 
and  under  0,  is  the  Log.  :  Thus  the  Log.  of  346  is  .53908  to 
which  prefix  2  for  the  Index,  because  there  are  three  places  of 
figures  in  the  whole  Number. 

If  the  given  Number  contains  four  figures,  the  first  three  are 
to  be  found,  as  before,  in  the  side  column,  and  under  the  fourth 
at  the  top  of  the  table  is  the  Log.  to  which  the  Index  3  is  to  be 
prefixed,  if  the  given  Number  is  an  Integer  :  Thus  the  Log.  of 
3467  is  .53995  to  which  prefix  3  for  the  Index. 

If  the  given  Number  exceeds  four  figures,  find  the  differ- 
ence between  the  Log.  of  the  first  four  figures,  and  the  next 
following  Log.  Multiply  this  difference  by  the  remaining  figure 
or  figures  in  the  given  Number;  point  off  as  many  figures  to 
the  right  hand  as  there  are  in  the  multiplier  ;  and  the  remain- 
der, added  to  the  Log.  of  the  first  four  figures,  will  be  the  re- 
quired Log. 

To  find  the  Number  corresponding  to  any  given  Logarithm. 


the  next  less  Log.  to  that  given  in  the  column  marked 
0  at  the  top,  and  continue  the  sight  along  that  horizontal  line, 
and  the  Log.  the  same  as  that  gives,  or  very  near  it,  will  be 
found  ;  then  the  first  three  figures  of  the  corresponding  Num.- 
ber  will  be  found  opposite,  in  the  first  side  column,  and  the 
fourth  figure  directly  above,  at  the  lop  of  the  page.  If  the 
Index  of  the  given  Log.  is  3,  the  four  figures  thus  found  are 
whole  numbers  ;  if  the  Index  is  2,  the  first  three  figures  are 
whole  numbers,  and  the  fourth  is  a  Decimal,  and  so  on. 

To  find  the  nearest  number  corresponding  to  any  Log.  for 
more  than  four  figures,  find  the  Log.  next  less  than  the  given 
one,  and  take  the  difference  between  that  and  the  given  one  ; 
also  take  the  difference  between  the  next  greater  and  the  next 
less  Log.  than  the  given  one  ;  divide  the  former  difference  by 
the  latter,  according  to  the  Rule  in  Division  of  Decimals  for 
dividing  a  le^s  number  by  a  greater  ;  add  the  Quotient  to  the 
number"  answering  to  the  Log.  next  less  than  the  given  one,  and 
you.  will  have  the  required  Number  ;  whether  a  whole,  or  a 
mixed  Number  will  be  determined  by  the  Index. 

The  addition  and  subtraction  of  Logarithms  answers  the 
game  purpose  as  the  multiplication  and  division  of  their  corres- 


LOGARITHMS.  3 

ponding  Numbers  :  That  is,  the  Log.  of  any  two  Numbers  be- 
ing added,  their  sum  will  be  the  Log.  of  the  Product  of  those 
Numbers  ;  and  the  Log.  of  one  Number  being  subtracted  from 
the  Log,  of  another  Number,  the  Remainder  will  be  the  Log. 
of  the  Quotient  of  one  of  those  Numbers  divided  by  the  other. 
Again,  the  Log.  of  any  Number  being  doubled  will  produce  the 
Log.  of  the  Square  of  that  number  ;  and  one  half  the  Log.  of 
any  Number  is  the  Log.  of  the  Square  Root  of  that  Number. 


II.  Of  the  Table  of  Logarithmic  or  Artificial  Sines,  Tangents^ 
and  Secants. 

To  find  the  Logarithmic  Sine,  fyc.for  any  number  of  Degrees 
find  Minutes,  within  the  compass  of  the  Table. 

If  the  Degrees  be  less  than  45,  look  for  them  at  the  top  of  the 
columns,  and  under  Sine,  Tangent  or  Secant,  whichever  is 
wanted,  and  for  the  Minutes  at  the  left  hand  ;  but  if  more  than 
45,  look  for  the  Degrees  at  the  bottom  over  Sine,  &c.  and  for 
the  Minutes  at  the  right  hand  ;  under  or  over  the  Degrees  and 
against  the  Minutes  will  be  the  required  Log.  Sine,  &c. 

To  find  the  Degrees  and  Minutes  corresponding  to  a  given 
Logarithmic  Sine,  fyc. 

Look  in  the  proper  column  for  the  nearest  Log.  to  the  given 
one  ;  and  the  Degrees  and  Minutes  standing  over  or  under  and 
against  it,  are  those  required. 

Note.  When  the  Log.  Sine,  &c.  for  more  than  90°  is  re- 
quired, subtract  the  given  number  of  Degrees  from  180°, 
and  make  use  of  the  Remainder. 

It  will  be  observed  that  this  Table  is  calculated  only  for  every 
o  Minutes.  This  was  thought  sufficient  for  Surveyors,  as  few 
Compasses  will  take  a  course  to  greater  exactness.  If,  how- 
ever, a  Question  is  to  be  solved  where  greater  accuracy  is  re- 
quired, work  by  natural  Sines.  Or, 

The  Log.  Sine,  fyc.for  any  Minute  may  be  found  as  follows: 
Look  in  the  Table  for  the  Log.  of  the  nearest  number  of 
Minutes  greater  than  the  given  one,  and  from  this  subtract  the 
next  less  Log.  contained  in  the  Table  :  Then  say,  as  5  Minutes, 
is  to  this  difference  ;  So  is  the  excess  of  the  given  Minutes 
above  5,  10,  15,  20,  25,  &c.  ;  To  a  fourth  number,  which  add 
to  the  Log.  of  the  Minutes  next  less  than  the  given  number,  and 
(he  sum  will  be  the  Log.  required. 


4  LOGARITHMS, 

EXAMPLE. 

Required  the  Logarithmic  Sine  of  34°  23' 

Sine  of  34°  25'  9.75221 

34   20  9.75128 

Difference  93 

As  5  :  93  :  :  3  :  56 

Sine  of  34°  20'  9.75128 

Add         -  56 

Sine  of  34°  23'  9.76184 

To  find  the  nearest  Minutes  corresponding  to  a  given  Loga 
rithtnic  Sine,  fyc. 

Look  in  the  Table,  in  the  proper  column,  for  the  Log.  next 
less  than  the  given  one,  and  take  the  difference  between  that 
and  the  given  one  ;  also  take  the  difference  between  the  next 
greater  and  the  next  less  Log.  than  the  given  one  ;  Then  say, 
As  the  latter  difference  ;  is  to  5  Minutes  ;  so  is  the  former  dif 
ierence ;  to  the  number  of  Minutes  to  be  added  to  the  Minute? 
of  the  Log.  next  less  than  the  given  one. 

EXAMPLE. 

Required  the  Degrees  and  Minutes  corresponding  to  the  Logarith 
mic  Tangent  9.73597. 

Given  Log.         9.73597     Next  greater  Log.         9.73627 
Next  less  9.73476  %  Next  less  -  9.7347G 


Difference     -         121  Difference  151 

As  151  :  5  :  :  121  :  4 

The  Degrees  and  Minutes  for  the  Log.  next  less  than  the 
given  one  are  28°  30'  to  which  add  4'  and  it  makes  28°  34'. 

JVofe.  As  after  the  most  careful  attention  of  the  Printers 
some  figures  in  the  Table  may  be  wrong  ;  and  as  some 
may  be  so  blurred  as  to  be  illegible,  let  it  be  observed, 
that  the  Sines  and  Co-Secants,  the  Co-Sines  and  Secants, 
and  the  Tangents  and  Co-Tangents,  standing  against  each 
other  respectively,  being  added  together,  will  amount  to 
20.00000,  if  the  Tables  are  accurate.  Thus  against  28^ 
20^  the  Sine  9.67533  added  to  the  Co-Secant  10.3236~ 


LOGARITHMS.  Q 

their  sum  is  20.00000  ;  so  also  is  the  sum  of  the  Co-Sine 
9.94458  and  the  Secant  10.05542,  and  likewise  the  sum  ot 
the  Tangent  9.73175  and  the  Co-Tangent  10.26825.  An 
error  may  consequently  be  easily  detected,  or  any  defaced 
figure  be  supplied. 


To  calculate  the  Northing  or  Southing,  fyc.for  any  Course  and 
Distance  by  Logarithms . 

This  is  done  by  the  first  CASE  of  RIGHT  ANGLED  TRIGONOME- 
TRY, as  follows  : 

Find  the  Log.  Sine  and  Co-Sine  of  the  Course ;  to  each  oi 
these  add  the  Log.  of  the  Distance  ;  subtract  Radius  or  10.00000 
from  their  sums,  and  the  remainders  will  be  the  Log.  of  the  re  • 
quired  Latitude  and  Departure, 

Note.  When  the  Angle  is  very  small  or  very  large,  and  the 
Distance  short,  the  sum  of  the  Log.  Sine  or  Co-Sine  and  the 
Log.  of  the  Distance  may  be  less  than  10.00000  or  Radi- 
us, which  cannot  therefore  be  subtracted.  In  such  cases 
look  for  the  Log.  without  regard  to  the  Index,  and  the  cor- 
responding number  will  be  a  Decimal,  the  first  figure  of 
which  will  be  tenths  if  the  Index  be  9,  and  hundredths  it 
the  Index  be  8. 


A  TABLE  OF  LOGARITHMS. 


No.  1—100.                 Log.  0.00000—2.00000. 

N. 

Log. 

M. 

Log, 

N. 

Log. 

N. 

Log.  N.|  Log. 

1 

0.00000 

21 

1.32222 

41 

.61278 

61 

1.78533 

81 

1.90849 

2 

0.30103 

22 

1.34242 

42 

.62325 

62 

1.79239 

82 

1.91381 

3 

0.47712 

23 

1.36173 

43 

.63347 

63 

1.79934 

83 

1.91908 

4 

0.60206 

24 

1.38021 

44 

.64345 

64 

1.80618 

84 

1.92428 

5 

0.69897 

25 

1.39794 

45 

.65321 

65 

1.81291 

85 

1.92942 

6 

0.77815 

26 

1.41497 

46 

.66276 

66 

1.81954 

86 

1.93450 

7 

0.84510 

27 

1.43136 

47 

.67210 

67 

1.82607 

87 

1.93952 

8 

0.90309 

28 

1.44716 

48 

.68124 

68 

1.85251 

88 

1.94448 

9 

0.95424 

29 

1.46240 

49 

.69020 

69 

1.83885 

89 

1.94939 

10 

1.00000 

30 

1.47712 

50 

.69897 

70 

1.84510 

90 

1.95.424 

11 

.04139 

31 

1.49136 

~5l 

.70757 

71 

1.85126 

91 

1.95904 

12 

.07918 

32 

1.50515 

52 

.71600 

72 

1.85733 

92 

1.96379 

13 

.11394 

33 

1.51851 

53 

.72428 

73 

1.86332 

93 

1.96848 

14 

.14613 

34 

1.53148 

54 

.73239 

74 

1.86923 

94 

1.97313 

15 

.17609 

35 

1.54407 

55 

.74036 

75 

1.87506 

95 

1.97772 

16 

.20412 

36 

1.55630 

56 

.74819 

76 

1.88081 

96 

1.98227 

17 

.23045 

37 

1.56820 

57 

.75587 

77 

1.88649 

97 

1.98677 

18 

.25527 

38 

1.57978 

58 

.76343 

78 

1.89209 

98 

1.99123 

19 

.27875 

39 

1.59106 

59 

1.77085 

79 

1.89763 

99 

1.99564 

20 

.30103 

40 

1.60206 

60 

1.77815 

80 

1.90309 

100 

2.00000? 

A  TABLE  OF  LOGARITHMS, 


7638  76 

1511  78981  7926  79 

152  8184  8213  82 

153  8469  8498  85 

154  8752  8780  88 
1551  9033  9061  90 

9312  9340  93 

1571  9590  9618  96 

158  9866  9893  99 

1591  01401201671  01 
0 


A  TABLE  OF  LOGARITHMS. 


No.  1600  —  2200.                 Log.  20412  —  34242. 

NO.   0 

1  |  2  ;  3 

4 

6  ;  6    7 

8 

y 

160 
161 

20412  20439 
0683  0710 

0466  20493 
0737  0763 

05205 
07901 

10548,20575 
081  7i  0844 

20602 
0871 

0629 
0898 

20656 
0925 

162 

0952!  0978 

1005;  1032 

1059 

1085  1112 

1139 

1165 

1192 

163 

1219  1245 

1272!  1299 

1325 

13521  1378 

1405 

1431 

1158 

164 

1484  1511 

1537.  1564 

1590 

1617  1643 

1669 

1696 

1722 

165 

1748  1775 

1801!  1827 

1854 

18801  1906 

1932 

1958 

1985 

66 

201  H  2037 

2063  2089 

2115 

2141;  2167 

2194 

2220 

2246 

57 

22721  2298 

2324  2350 

2376 

2401  j  2427 

2453 

2479 

2505 

168 

2531!  2557 

2583|  2608 

2634 

2660:  2686 

2712 

2737 

2763 

169 

2789!  2814 

2840;  2866 

2891 

2917;  2943 

2968 

2994 

3019 

170 

3045:  3070 

3096  3121 

3147 

3172^  3198 

13223 

3249 

3274 

171 

3300  3325 

3350i  3376 

3401 

3426  3452 

3477 

3502 

3528 

172 

3553  3578 

3603  3629 

S654 

3679  3704 

3729 

3754 

3779 

173 

3805  3830 

3855  3880 

3905 

3930  3955 

3980 

4005 

4030 

174 

4055  4080 

4105;  4130 

4155 

4180  4204 

4229 

4254 

4279 

175 

4304  4329 

4353  4378 

4403 

4428.  4452 

4477 

4502 

4527 

176 

4551  4576 

4601,  4625 

4650 

46741  4699 

4724 

4748 

4773 

177 

4797  4822 

4846  4871 

4895 

4920  4944 

4969 

4993 

5018 

178 

5042  5066 

5091  '  5115 

5139 

5164  5188 

5212 

5237 

5261 

179 

5285 

5310 

5334  5358 

5382 

5406;  5431 

5455 

5479 

5503 

180 

5527 

5551 

5575  5600 

5624 

5648  5672 

5696 

"6720 

5744 

181 

5768 

5792 

5816i  5840 

5864 

5888  5912 

5935 

5959 

5983 

182 

6007 

6031 

6055;  6079 

6102 

6126  6150 

6174 

6198 

6221 

183 

6245 

6269 

6293  6316 

6340 

6364  6367 

6411 

6435 

6456 

184 

6482 

6505 

6529  6553 

6576 

6600 

6623 

6647 

6670 

6694 

185 

6717 

6741 

6764,  6788 

6811 

6834 

6858 

6881 

6905 

6928 

186 

6951 

6975 

6998i  7021 

7045 

7068 

7091 

7114 

7138 

7161 

187 

7184 

7207 

7231!  7264 

7277 

7800 

7323 

7346 

7370 

7393 

188 

7416 

7439 

7462  748,3 

7508 

7531 

7554 

7577 

7600 

7623 

189 

7646 

7669 

76921  7715 

7738 

7761 

7784 

7807 

7830 

7852 

190 

7875 

7898 

~792ii^7944 

7967 

7989 

8012 

"8036 

8058 

8081 

191 

8103 

8126 

8149  8171 

8194 

8217 

8240 

8262 

8285 

8307 

192 

8330 

8353 

8375 

8398 

8421 

8443 

846b 

8488 

8511 

8533 

193 

8556 

8578 

8601 

8623 

8646 

8668 

8691 

8713 

8735 

8758 

19' 

8780 

8803 

8825 

8847 

8870 

8892 

8914 

8937 

8959 

8981 

195>  9003 

9026  9048 

9070!  9092 

9115 

9137 

9159 

9181 

9203 

196  9226 

9248  9270 

9292!  9314 

9336 

9358J  9380 

9403 

9425 

197  9447 

9469  9491 

9513 

9535 

9557 

9579  960 

9623J  9645 

198  9667 

9688  9710 

9732 

9754  9776 

97981  9820 

9842'  9863 

199)  9885 

9907 

9929 

9951 

9973)  9994 

30016'  3003c 

3006030081 

WO  30103 

30125 

30146 

30168  '30190  '30211 

0233'  ~02fo 

0276  0276 

201 

0320 

0341 

0364 

0384  0406  0428 

0449',  047 

0492  0514 

202 

0535 

0557 

0578 

OGOOi  06211  0643 

0664  068 

0707 

0728 

203 

0750 

0771 

0792 

0814 

0835  0856 

0878  089 

0920 

094£ 

204  0963 

0984 

1006 

1027 

1048  1069 

1091;  111 

1133 

1154 

205 

1175 

1197 

1218 

1239 

1260  1281 

1302  132 

1345 

1366 

206 

.  1387 

1408 

1429 

1450!  1471  1492 

1513  1534 

1555 

1576 

20- 

r  1597 

1618 

1639 

1660 

1681  1702 

1723'  1744 

1765 

1785 

205 

]  1806 

1827 

1848 

1869 

1890  1911 

193i;  195 

1973 

1994 

20< 

1  2015 

2035 

2056 

2077 

2098  2118 

2139  216 

2181 

2201 

21( 

j  2222 

"2242 

2263 

2284 

2305 

2325 

~2346~23<F 

2387 

~2408 

£1 

I  2428 

244£ 

1  2469 

24901  2510 

2531 

2552  257 

2592 

2613 

212  2634 

265^ 

2675 

2695  2715 

2736 

2756  277 

279' 

2818 

213;  2838 

285* 

2879 

2899  2919 

2940 

2960  298 

S001 

3021 

214!  3041 

3062 

3082 

3102 

3122 

3143 

3163  318, 

320l 

3224 

215  3244 

326^ 

[  3284 

3304 

[  3325 

3345 

3365  338 

340£ 

3425 

216  3446 

346i 

»  3486 

350( 

.  3526 

3546 

3566  358 

3606 

3626 

217  3646 

366( 

>  3686 

370f 

t  3726 

3746 

3766  378 

380( 

3826 

218'  38-16 

386( 

5  3885 

390^ 

>  392£ 

3945 

3965  398 

400c 

4025 

219  404- 

406^ 

I  4'  84 

4K> 

I  4124 

4143 

4168  418 

420^ 

4223 

«*oT  0 

1    2 

~3~ 

4 

5 

6  '  7 

~~8~ 

9 

A  TABLE  OF  LOGARITHMS. 


No.  .220O—  2800.                Log.  34242—  44716. 

NO. 

0 

1 

2 

3 

4    5 

6 

7    8  i  9 

220 

34242 

34262 

4282 

34301 

3432134341 

34361 

34380  34400  344201 

221 

4439 

4459 

4479 

4498 

4518  4537 

4557 

4577 

4596J  4616 

222 

4635 

4655 

4674 

4694 

4713  4733 

4753 

4772 

4792  4811 

223 

4830 

4850 

4869 

4889 

4908  4928 

4947 

4967  498"6|  5005 

224 

5025 

5044 

5064 

5083 

5102  5122 

5141 

51601  5180!  5199 

225 

5218[  5238 

6257 

5276 

5295  5315 

5334 

5353 

5372!  5392 

226 

5411 

5430 

5449 

5468 

5488  5507 

5526 

5545 

5564 

5583 

227 

5603 

5622 

5641 

5660 

5679  5698 

5717 

5736 

5755 

5774 

228 

5793 

5813 

5832 

5851 

5870 

5889 

5908 

5927 

5946 

5965 

229 

5984 

6003 

6021 

6040 

6059 

6078 

6097 

6116 

6135 

6154 

230 

6173 

6192 

6211 

"6229 

6248 

6367 

6286 

6305  6324 

6342 

231 

6361 

6380 

6399 

6418 

6436 

6455 

6474 

6493i  6511 

6530 

232 

6549 

6568 

6586 

6605 

6624 

6642 

6661 

66801  6698 

6717 

233 

6736 

6754 

6773 

6791 

6810 

6829 

6847 

6866i  6884!  6903 

234 

6922 

6940 

6959 

6977 

6996 

7014 

7033 

70511  7070'  7088 

235 

7107 

7125 

7144 

7162 

7181 

7199 

7218 

7236:  7254)  7273 

236 

7291 

7310 

7328 

7346 

7365 

7383 

7401 

7420|  7438  7457 

237 

7475 

7493 

7511 

7530 

7548 

7566 

7585 

7603  7621)  7639 

238 

7658 

7676 

7694 

7712 

7731 

7749 

7767 

7785 

7803  7822 

239 

7840 

7858 

7876 

7894 

7912 

7931 

7949 

7967 

7985!  8003 

240 

8021 

8039 

8057 

8075 

8093 

8112 

8130 

"8148 

8166i~8184 

241 

8202 

8220 

8238 

8256 

8274 

8292 

8310 

8328J  83461  8364 

242 

8382 

8399 

8417 

8435 

8453 

8471 

8489 

8507  8525!  8543 

243 

8561 

8578 

8596 

8614 

8632 

8650 

8668 

8686!  8703!  8721 

244 

8739 

8757 

8775 

8792 

8810 

8828 

8846 

8863 

8881  i  8899 

245 

8917 

8934 

8952 

8970 

8987 

9005 

9023 

9041 

9058  9076 

246 

9094 

9111 

9129 

9146 

9164 

9182 

9199 

9217 

9235  9252 

247 

9270 

9287 

9305 

9322 

9340 

9358 

9375 

9393 

9410  9428 

248 

9445 

9463 

948ff 

9498 

9515 

9533 

9550 

9568'  9585  9602 

249 

9620 

9637 

9655 

9672 

9690 

9707 

9724 

9742,  9759j  9777 

250 

"9794 

9811 

9829 

9846 

9863 

9881 

9898 

9915,  9933,  9950 

251 

9967 

9985 

40002 

40019 

40037 

40054 

40071 

40088  40106  40123 

252 

40140 

40157 

0175 

0192 

0209 

0226 

0243 

0261  i  0278 

0295 

253 

0312 

0329 

0346 

0364 

0381 

0398 

0415 

04321  0449 

0466 

254 

0483 

0500 

0518 

0535 

0552 

0569 

0586 

0603 

0620 

0637 

25o 

0654 

0671 

0688 

0705 

0722 

0739 

0756 

0773 

0790 

0807 

256 

0824 

0841 

0858 

0875 

0892 

0909 

0926 

0943 

0960 

0976 

257 

0993 

1010 

1027 

1044 

1061 

1078 

1095 

1111 

11?8 

1145 

258 

1162 

1179 

1196 

1212 

1229 

1246 

1263 

1280 

1296 

1313 

259 

1330 

1347 

1363 

1380 

1397 

1414 

1430 

1447 

1464 

1481 

260 

1497 

1514 

1531 

1547 

1564 

158 

1597 

1614 

1631 

1647 

26 

1664 

168 

1697 

1714 

1731 

1747 

1764 

1780 

1797 

1814 

262 

1830 

1847 

1863 

1880 

1896 

1913 

1929 

1946 

1963 

1979 

263 

1996 

2012 

2029 

2045 

206L 

2078 

2095 

2111 

2127 

2144 

264 

2160 

2177 

2193 

2210 

2226 

2243 

2259 

2275 

2292 

2308 

26 

2325 

234 

2357 

237o 

2390 

2406 

2423 

2439 

2455 

2472 

26 

2488 

2504 

252 

2537 

2553 

2570 

2586 

2602 

2619 

2635 

26 

2651 

266 

2684 

2700 

2716 

2732 

2749 

2765 

2781 

2797 

26 

2813 

2830 

2846 

2862 

2878 

2894 

2911 

2927 

2943 

2959 

26 

2975 

299 

3008 

3024 

3040 

3056 

3072  3088 

3104 

3120 

27" 

~3136 

~3l52 

3169 

3185 

"3*0" 

3217 

3233!  3249)  3265 

3281 

27 

3297 

331 

3329!  3345 

336 

3377 

3393 

3409!  3425 

3441 

27 

3457 

3473 

3489  3505J  3521 

3537 

3553 

3569  3584 

3600 

27 

3S16 

363 

3648!  3664!  3680 

3696 

3712 

3727  3743 

3759 

27 

3775 

379 

3807 

3823  3838 

3854 

3870 

3886 

3902 

3917 

27 

3933 

394 

3965 

3981 

3996 

4012 

4028 

4044 

4059 

4075 

276 

•  4091 

4HK 

41221  4138 

4154 

4170 

4185 

4201 

4217 

4232 

27' 

r  4248 

4264 

[  4279:  4295 

431 

4326 

4342 

4358 

4373 

4389 

¥K 

5  4404 

442C 

>  4436|  4451 

4467 

4483 

4498 

4514 

4529 

4545 

m 

>  456C 

4576 

>  4592  4607 

4623 

463 

4654 

4669 

4685 

4700 

tfO 

0 

1    213 

4 

5 

6 

7 

9 

A  TABLE  OF  LOGARITHMS. 


JNo.  2800  —  3400.                 Log.  44716  —  53148. 

xo 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

28C 

44716 

4473" 

4474 

44762 

4477S 

44793 

44809'  44824 

44840 

44855 

28 

487 

488 

49^ 

491 

4932 

4948 

4963  4979 

4994 

5010 

28 

5025 

5040 

505 

507 

508( 

5102 

5117  5133 

5148 

5163 

28 

5179 

5194 

520 

522o 

524C 

5255 

52711  5286 

530 

5317 

28 

5332 

5347 

536 

5378 

539£ 

5408 

5423  5439 

5454 

5469 

28 

5484 

5500 

5516 

5530 

554i 

5561 

5576|  559 

5606 

5621 

28 

5637 

565'. 

566 

5682 

569' 

5712 

5728 

5743 

5758 

5773 

28 

5788 

5803 

5818 

5834 

584£ 

5864 

587 

5894 

5909 

5924 

28 

5939 

595' 

5969 

5934 

600C 

6015 

6030 

6045 

6060 

6075 

28 

6090 

610a 

6120 

6135 

6I5C 

6165 

6180 

619o 

6210 

6225 

29C 

"6240 

625o 

6270 

6285 

630C 

6315 

"6330 

"6345 

6359 

"6374 

29 

6389 

640^ 

6419 

6434 

644£ 

6464 

6479 

6494 

6509 

6523 

29' 

6538 

6553 

6568 

6583 

659S 

6613 

6627 

6642 

6657 

6672 

293 

6687 

6702 

6716 

6731 

6746 

6761 

6776 

6790 

6805 

6820 

294 

6835 

6850 

6864 

6879 

6894 

6909 

6923 

6938 

6953 

6967 

29o 

6982 

6997 

7012 

7026 

7041 

7056 

7070 

7085 

7100 

7114 

296 

7129 

7144 

7159 

7173 

7188 

7202 

7217 

7232 

7246 

7261 

297 

7276 

7290 

7305 

7319 

7334 

7349 

7363 

7378 

7392 

7407 

298 

7422 

7436 

7451 

7465 

7480 

7494 

7509 

7524 

7538 

7553 

299 

7567 

7582 

7596 

7611 

7625 

7640 

7654 

7669 

7683 

7698 

300 

7712 

7727 

7741 

7756 

7770 

7784 

"7799 

7813 

7828 

7842 

301 

7857 

7871 

7835 

7900 

7914 

7929 

7943 

7958 

7972 

7986 

302 

8001 

8015 

8029 

8044 

8058 

8073 

8087 

8101 

8116 

8130 

303 

8144 

8159 

sr/3 

8187 

8202 

8216 

8230 

8244 

8259 

8273 

304 

8287 

8302 

8316 

8330 

8344 

8359 

8373 

8387 

8401 

8416 

305 

8430 

8444 

8458 

8473 

8487 

8501 

8515 

8530 

8544 

8558 

306 

8572 

8586 

8601 

8615 

8629 

8643 

8657 

8671 

8686 

8700 

307 

8714 

8728 

8742 

8756 

8770 

8785 

8799 

8813 

8827 

8841 

308 

8855 

8869 

8883 

8897 

8911 

8926 

8940 

8954 

8968 

8982 

309 

8996 

9010 

9024 

9038 

9052 

9066 

9080 

9094 

9108 

9122 

310 

9136 

9150 

9164 

"9178 

9192 

9206 

9220 

9234 

"9248 

9262 

311 

9276 

9290 

9304 

9318 

9332 

9346 

9360 

9374 

9388 

9403 

312 

9415 

9429 

9443 

9457 

9471 

9485 

9499 

9513 

9527 

9541 

313 

9554 

9568 

9582 

9596 

9610 

9624 

9838 

9651 

9665 

9679 

314 

9693 

9707 

9721 

9734 

9748 

9762 

9776 

9790 

9803 

9817 

315 

9831 

9845 

9859 

9872 

9886 

9900 

9914 

9927 

9941 

9955 

316 

9969 

9982 

9996 

0010 

o0024 

50037 

50051 

50065 

50079 

50092 

317 

0106 

50120 

0133 

0147 

0161 

0174 

0188 

0202 

0215 

0229 

318 

0243 

0256 

0270 

0284 

0297 

0311 

0325 

C333 

0352 

0365 

319 

0379 

0393 

0406 

0420 

0433 

0447 

0461 

0474 

0488 

05W 

320 

0515 

0529 

0542 

0556 

0569 

0583 

0596 

0610 

0323 

"0637 

321 

0651 

0664 

0678 

0691 

0705 

0718 

0732 

0745 

0759 

0772 

322 

0786 

0799 

0813 

0826 

0840 

0853 

0866 

0880 

0893 

0907 

323 

0920 

0934 

0947 

0961 

0974 

0987 

1001 

1014 

1028 

1041 

324 

1055 

1068 

1081 

1095 

1108 

1121 

1135 

1148 

1162 

1175 

325 

1188 

1202 

1215 

1228 

1242 

1255 

1268 

1282 

1295 

1308 

326 

1322 

1335 

1348 

1362 

1375 

1388 

1402 

1415 

1428 

1441 

327 

1455 

1468 

1481 

1495 

1508 

1521 

1534 

1548 

1561 

1574 

328 

1587 

1601 

1614 

1627 

1640 

1654 

1667 

1680 

1693 

1706 

329 

1720 

1733 

1746 

1759 

1772 

1786 

1799 

1812 

1825 

1838 

330 

"1851 

1865 

1878 

1891 

1904 

"1917 

1930 

1943 

1957 

1970 

331 

1983 

1996 

2009 

2022 

2035 

2048 

2061 

2075 

2088 

2101 

332 

2114 

2127 

2140 

2153 

2166 

2179 

2192 

2205 

2218 

2231 

333 

2244 

2257 

2270 

2284 

2297 

2310 

2323 

2336 

2349 

2362 

334 

2375 

2388 

2401 

2414 

2427 

2440 

2453 

2466 

2479 

2492 

335 

2504 

2517 

2530 

2543 

2556 

2569 

2582 

2595 

2608 

2621 

336 

2634 

2647 

2660 

2673 

2686 

2699 

2711 

2724 

2737 

2750 

337 

2763 

2776 

2789 

2802 

2815 

2827 

2840 

2853 

2866 

2879 

338 

2892 

2905 

2917 

2930 

2943 

2956 

2969 

2982 

2991 

3007 

339 

3020 

3033 

3046 

3058 

3071 

3084 

3097 

3110 

3122 

3135 

NO. 

0 

1 

2 

3 

~T" 

5 

6 

7 

8 

9 

A  TABLE  OF  LOGARITHMS. 


No,  3400  —  4000.                 Log.  53148  —  60206. 

No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

340 

3148, 

^5161 

33173J53186 

53199 

3212 

3224 

3237 

3250 

.3263 

341 

3275 

S288 

3301  3314 

3326 

3339 

3352 

3364 

3377 

3390 

342 

3403 

3415 

3428  3441 

3453 

3466 

3479 

3491 

3504 

3517 

343 

3529 

3542 

3555 

3567 

3580 

3593 

3605 

3618 

3631 

3643 

34-1 

3656 

3668 

3681 

3694 

3706 

3719 

3732 

3744 

3757 

3769 

345 

3782 

3794 

3807 

3820 

3832 

3845 

3857 

3870 

3882,  3895 

346 

3908! 

3920 

3933 

3945 

3958 

3970 

3983 

3995 

4008J  4020 

347 

4033 

4045 

4058 

4070 

4083 

4095 

4108 

4120 

4133  4145 

348 

4158 

4170 

4183 

4195 

4208 

4220 

4233 

4245 

4258 

4270 

349 

4283 

4295 

4307 

4320 

4332 

4345 

4357 

4370 

4382 

4394 

350 

4407 

4419 

4432 

4444 

4456 

4469 

4481 

4494 

4506 

4518 

351 

4531 

4543 

4555 

4568 

4580 

4593 

4605 

4617 

4630 

4642 

352 

4654 

4667 

4679 

4691' 

4704 

4716 

4728 

4741 

4753 

4765 

353 

4777 

4790 

4802 

4814 

4827 

4839 

4851 

4864 

4876 

4888 

354 

4900 

4913 

4925 

4937 

4949 

4962 

4974 

4986 

4998 

5011 

355 

5023 

5035 

5047 

5060 

5072 

5084 

5096 

5108 

6121 

5133 

356 

5145 

5157 

5169 

5182 

5194 

5206 

5218 

5230 

5242 

5255 

357 

5267 

5279 

5291 

5303 

5315 

5328 

5340 

5352 

5364 

5376 

358 

5388 

5400 

5413 

5425 

5437 

5449 

5461 

5473 

5485 

5497 

359 

5509 

5522 

5534 

5546 

5558 

5570 

5582 

5594 

5606 

5618 

360 

5630 

5642 

5654 

5666 

5678 

5691 

5703 

5715 

5727 

5739 

361 

5751 

5763 

5775 

5787 

5799 

5811 

5823 

5835 

5847 

5859 

362 

5871 

5883 

5895 

5907 

5919 

5931 

5943 

5955 

5967 

5979 

363 

5991 

6003 

6015 

6027 

6038 

6050 

6062 

6074 

6086 

6098 

364 

6110 

6122 

6134 

6146 

6158 

6170 

6182 

6194 

6205 

6217 

365 

6229 

6241 

6253 

6265 

6277 

6289 

6301 

6312 

6324 

6336 

366 

6348 

6360 

6372 

6384 

6396 

6407 

6419 

6431 

6443 

6455 

367 

6467 

6478 

6490 

6502 

6514 

6526 

6538 

6549 

6561 

6573 

368 

6585 

6597 

6608 

6620 

6632 

6644 

6656 

6667 

6679 

6691 

369 

6703 

6714 

6726 

6738 

6750 

6761 

6773 

6785 

6797 

6808 

370 

6820 

6832 

6844 

6855 

6867 

6879 

"689" 

6902 

6914 

6926 

371 

6937 

6949 

6961 

6972 

6984 

6996 

7008 

7019 

7031 

7043 

372 

7054 

7066 

7078 

7089 

7101 

7113 

7124 

7136 

7148 

7159 

373 

7171 

7183 

7194 

7206 

7217 

7229 

724 

7252 

7264 

7276 

374 

'  7287 

7299 

7310 

7322 

7334 

734o 

735 

7368 

7380 

7392 

375 

7403 

7415 

7426 

7438 

7449 

7461 

7473 

7484 

7496 

7507 

376 

7519 

7530 

7542 

7553 

7565 

7576 

758 

7600 

7611 

7623 

37" 

7634 

7646 

7657 

7669 

7680 

7692 

7703 

7715 

7726 

7738 

378 

7749 

7761 

7772 

7784 

7795 

7807 

7818 

7830 

7841 

7852 

379 

7864 

7875 

7887 

7898 

7910 

792 

7933 

794 

7955 

7967 

380 

7978 

7990 

8001 

8013 

8024 

8035 

8047 

805 

8070 

8081 

381 

8092 

8104 

8115 

8127 

8138 

8149 

8161 

817 

8184 

8195 

382 

8206 

8218 

8229 

8240 

8252 

8263 

8274 

828 

8297 

8309 

383 

8320 

8331 

8343 

8354 

8365 

8377 

8388 

839 

8410 

8422 

384 

8433 

8444 

8456 

8467 

8473 

8490 

8501 

851 

8524 

8535 

385 

8546 

8557 

8569 

8580 

859 

8602 

8614 

862 

8636 

8647 

386 

8659 

8670 

8681 

8692 

8704 

871 

8726 

873 

874< 

8760 

387 

8771 

8782 

8794 

8805 

881 

882 

8838 

885 

886 

8872 

38 

8883 

8894 

8906 

8917 

892 

893 

895C 

896 

8973 

8984 

389 

8995 

9006 

9017 

9028 

904C 

905 

9062 

907 

9084 

9096 

390 

9106 

9118 

9129 

9140 

915 

916 

9173 

918 

9195 

9207 

391 

9218 

9229 

9240 

9251 

926 

927 

9284 

929 

930 

9318 

392 

9329 

9340 

935 

9362 

937 

9384 

9395 

940 

941 

9428 

392 

9439 

9450 

946 

9472 

9483 

9494 

9506 

951 

952 

9539 

394 

9550 

9561 

9572 

9583 

959 

9605 

9616 

962 

963 

9649 

39£ 

9660 

9671 

9682 

969S 

970 

9715 

9726 

973 

974 

9759 

396 

9770 

978C 

979 

9802 

9813 

9824 

9835 

984 

985 

9868 

39" 

9879 

989C 

990 

9912 

9923 

9934 

9945 

995 

996 

9977 

39* 

9988 

9999 

600K 

60021 

6003 

60043 

60054 

6006 

6007 

60086 

39t 

60097 

60108 

0118 

013C 

014 

0152 

0163 

0173 

0184 

0195 

NO 

0 

1 

2 

~3~ 

4 

5 

6 

7 

~~S~ 

9 

A  TABLE  OF  LOGARITHMS. 


11 


]So.  4000  —  4600.                 Log.  60206  —  66276. 

NO. 

0 

1  1 

2 

3 

4 

5 

6    7 

8 

9 

400 

0206 

0217 

0228 

0239 

0249 

60260 

"027160282 

S0293 

0304 

401 

0314 

0325 

0336 

0347 

0358 

0369 

0379 

0390 

0401 

0412 

40-2 

0423 

0433 

0444 

0455 

0466 

0477 

0487 

0498 

0509 

0520 

403 

0531 

oki 

0'52 

0563 

0574 

0584 

0595 

0606 

0617 

0627 

404 

0638 

0649 

0660 

0670 

0681 

0692 

0703 

0713 

0724 

0735 

405 

0746 

0756 

0767 

0778 

0788 

0799 

0810 

0821 

0831 

0842 

406 

0853 

0863 

0874 

0885 

0895 

0906 

0917 

0927 

0938 

0949 

407 

0959 

0970 

0981 

0991 

1002 

1013 

1023 

1034 

1045 

1055 

408 

1066 

1077 

1087 

1098 

1109 

1119 

1130 

1140 

1151 

1162 

409 

1172 

1188 

1194 

1204 

1215 

1225 

1236 

1247 

1257 

1268 

410 

1278 

1289 

1300 

1310 

1321 

1331 

1342 

1352 

1363 

1374 

411 

1384 

1395 

1405 

1416 

1426 

1437 

1448 

1458 

1469 

1479 

412 

1490 

1500 

1511 

1521 

1532 

1542 

1553 

1563 

1574 

1584 

413 

1595 

1606 

1616 

1627 

1637 

1648 

1658 

1669 

1679 

1690 

414 

1700 

1711 

1721 

1731 

1742 

1752 

1763 

1773 

1784 

1794 

415 

1805 

1815 

1826 

1836 

1847 

1857 

1868 

1878 

1888 

1899 

416 

1909 

1920 

1930 

1941 

1951 

1962 

1972 

1982 

1993 

2003 

417 

2014 

2024 

2034 

2045 

2055 

2066 

2076 

2086 

2097 

2107 

418 

2118 

2128 

2138 

2149 

2159 

2170 

2180 

2190 

2201 

2211 

419 

2221 

2232 

2242 

2252 

2263 

2273 

2284 

2294 

2304 

2315 

420 

"2325 

"2335 

2346 

"2356 

"2366 

1377 

2387 

2397 

2408 

2418 

421 

2428 

2439 

2449 

2459 

2469 

2480 

2490 

2500 

2511 

2521 

422 

2531 

2542 

2552 

2562 

2572 

2583 

2593 

2603 

2613 

2624 

423 

2634 

2644 

2655 

2665 

2675 

2685 

2696 

2706 

2716 

2726 

424 

2737 

2747 

2757 

2767 

2778 

2788 

2798 

2808 

2818 

2829 

425 

2839 

2849 

2859 

2870 

2880 

2890 

2900 

2910 

2921 

2931 

426 

2941 

2951 

2961 

2972 

2982 

2992 

3002 

3012 

3022 

3033 

427 

3043 

3053 

3063 

3073 

3083 

3094 

3104 

3114 

3124 

3134 

428 

3144 

3155 

3165 

3175 

3185 

3195 

3205 

3215 

3225 

3236 

429 

3246 

3256 

3266 

3276 

3286 

3296 

3306 

3317 

3327 

3337 

430 

3347 

"3357 

3367 

3377 

"3387 

3397 

3407 

3417 

3428 

3438 

431 

3448 

3458 

3468 

3478 

3488 

3498 

3508 

3518 

3528 

3538 

432 

3548 

3558 

3568 

3579 

3589 

3599 

3609 

3619 

3629 

3639 

433 

3649 

3659 

3669 

3679 

3689 

3699 

3709 

3719 

3729 

3739 

434 

3749 

3759 

3769 

3779 

3789 

3799 

3809 

3819 

3829 

3839 

435 

3849 

3859 

3869 

3879 

3889 

3899 

3909 

3919 

3929 

3939 

436 

3949 

3959 

3969 

3979 

3988 

3998 

4008 

4018 

4028 

4038 

437 

4048 

4058 

4068 

4078 

4088 

409 

4108 

4118 

4128 

4137 

438 

4147 

4157 

4167 

4177 

418" 

419 

4207 

4217 

4227 

4237 

439 

4246 

4256 

4266 

4276 

4286 

4296 

4306 

4316 

4326 

4335 

440 

434o 

4355 

4365 

4375 

4385 

4395 

4404 

4414!  4424 

4434 

441 

4444 

4454 

4464 

4473 

4483 

4493 

4503 

4513  4523 

4532 

442 

454" 

4552 

4562 

4572 

4582 

459 

4601 

4611 

4621 

4631 

443 

4640 

4650 

4660 

4670 

468C 

468 

4699 

4709 

4719 

4729 

444 

473 

4748 

4758 

4768 

477" 

478 

4797 

4807 

4816 

4826 

44* 

483 

484 

485 

4865 

487S 

•488 

4895 

4904 

4914 

4924 

446 

493 

494 

4953 

4963 

4972 

498 

4992 

5002 

5011 

5021 

44 

503 

504 

5050 

5060 

507C 

507 

5089 

5099 

5108 

5118 

44 

512 

513 

514 

5157 

5167 

517 

5186 

5196 

5205 

5215 

44 

522 

523 

5244 

5254 

5263 

5273 

5283 

6292 

5302 

5312 

45 

5321 

533 

534 

5350 

536C 

5369 

5379 

5389 

5398 

5408 

45 

541* 

i  542 

543 

5447 

5456 

546 

5475 

5485 

5495 

5504 

45 

551^ 

I  552 

553 

5543 

5552 

5562 

5571 

5581 

5591 

5600 

46 

56K 

)  561 

562 

5639 

5648 

5658 

5667 

5677 

5686 

5696 

454 

570( 

5  571 

572 

5734 

5744 

5753 

5763 

5772 

5782 

5792 

45 

5801 

581 

582C 

5830 

5839 

5849 

5858 

5868 

5877 

5887 

45 

589< 

>  5906 

591 

5925 

5935 

5944 

5954 

5963 

5973 

5982 

45 

5995 

>  600 

601 

6020 

6030 

6039 

6049 

6058 

6068 

6077 

45 

608 

7  609 

610 

6115 

6124 

6134 

6143 

6153 

6162 

6172 

45 

618 

I  619 

620C 

6210 

6219 

6229 

6238 

6247 

625" 

6266 

NO 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

A  TABLE  OF  LOGARITHMS. 


No.  4600  —  52CO.                 Log.  66276  —  71600. 

NO. 

0 

1 

2 

3 

4 

5 

6    7 

8 

9 

460 

66276 

66285 

66295 

66304 

66314 

66523 

6633266342 

66351 

66361 

461 

6370 

6380 

6389 

6398 

6408 

6417 

6427J  6436 

6445 

6455 

462 

6464 

6474 

6483 

6492 

6502 

6511 

65211  6530 

6539 

6549 

463 

6558 

6567 

6577 

6586 

6596 

6605 

6614  6624 

6633 

6642 

464 

6652 

6661 

6671 

6680 

6689 

6699 

6708!  6717 

6727 

6736 

465 

6745 

6755 

6764 

6773 

6783 

6792 

6801  6811 

6820 

6829 

466 

6839 

6848 

6857 

6867 

6876 

6885 

6894'  6904 

6913 

6922 

467 

6932 

6941 

6950 

6960 

6969 

6978 

6987  i  6997 

7006 

7015 

468 

7025 

7034 

7043 

7052 

7062 

7071 

70801  7089 

7099 

7108 

469 

7117 

7127 

7136 

7145 

7154 

7164 

7173,  7182 

7191 

7201 

470 

7210 

7219 

7228 

7237 

7247 

7256 

7265  i  7274 

7284 

7293 

471 

7302!  7311 

7321 

7330 

7339 

7348 

7357;  7367 

7376 

7385 

472 

7394 

7403 

7413 

7422 

7431 

7440 

7449  7459 

7468 

7477 

473 

7486 

7495 

7504 

7514 

7523 

7532 

7541  i  7550 

756C 

7569 

474 

7578 

7587 

7596 

7605 

7614 

7624 

7633,  7642 

7651 

7660 

475 

7669 

7679 

7688 

7697 

7706 

7715 

7724  7733 

7742 

7752 

476 

7761 

7770 

7779 

7788 

7797 

7806 

7815|  7825 

7834 

7843 

477 

7852 

7861 

7870 

7879 

7888 

7897 

7906:  7916 

7925 

7934 

478 

7943 

7952 

7961 

7970 

7979 

7988 

79971  8006 

8015 

8024 

479 

8034 

8043 

8052 

8061 

8070 

8079 

8088  i  8097 

8106 

8115 

480 

~8~l24 

"8133 

"8142 

8151 

8160 

8169 

8178:  8187 

8196 

8205 

481 

8215 

8224 

8233 

8242 

8251 

8260 

8269'  8278 

8287 

8296 

482 

8305 

8314 

8323 

8332 

8341 

8350 

8359  i  8368 

8377 

8386 

483 

8395 

8404 

8413 

8422 

8431 

8440 

8449i  8458 

8467 

8476 

484 

8485 

8494 

8502 

8511 

8520 

8529 

8538 

8547 

8556 

8565 

485 

8574 

8583 

8592 

8601 

8610 

8619 

8628 

8637 

8646 

8655 

486 

8664 

8673 

8681 

8690 

8699 

8708 

8717 

8726 

8735 

8744 

487 

8753 

8762 

8771 

8780 

8789 

8797 

8806 

8815 

8824 

8833 

488 

8842 

8851 

8860 

8869 

8878 

8886 

8895 

8904 

8913 

8922 

489 

8931 

8940 

8949 

8958 

8966 

8975 

8984 

8993 

9002 

9011 

490 

9020 

9028 

9037 

9046 

9055 

9064 

9073 

9082 

9090 

9099 

491 

9108 

9117 

9126 

9135 

9144 

9152 

9161 

9170 

9179 

9188 

492 

9197 

9205 

9214 

9223 

0232 

9241 

9249 

9258 

9267 

9276 

193 

9285 

9294 

9302 

9311 

9320 

9329 

9338 

9346 

9355 

9364 

494 

9373 

9381 

9390 

9399 

9408 

9417 

9425 

9434 

9443 

9452 

495 

9461 

9469 

9478 

9487 

9496 

9504 

9513 

9522 

9531 

9539 

496 

9548 

9557 

9566 

9574 

9583 

9592 

9601 

9609 

9618 

9627 

497 

9636 

9644 

9653 

9662 

9671 

9679 

9688 

9697 

9705 

9714 

498 

9723 

9732 

9740 

9749 

9758 

9767 

9775 

9784 

9793 

9801 

499 

9810 

9819 

9827 

9836 

9845 

9854 

9862 

9871 

9880 

9888 

500 

9897 

9906 

9914 

9923 

9932 

9940 

9949 

9958 

9966 

9975 

501 

9984 

9992 

70001 

70010 

70018 

70027 

70036 

70044 

70053 

70062 

502 

70070 

70079 

0088 

0096 

0105 

0114 

0122 

0131 

0140 

0148 

503 

0157 

0165 

0174 

0183 

0191 

02001  0209 

0217 

0226 

0234 

504 

0243 

0252 

0260 

0269 

0278 

0286i  0295 

0303 

0312 

0321 

505 

0329 

0338 

0346 

0355 

0364 

0372 

0381 

0389 

0398 

0406 

506 

0415 

0424 

0432 

0441 

0449 

0458 

0467 

0475 

0484 

0492 

507 

0501 

0509 

0518 

0526 

0535 

0544 

0552 

0561 

0569 

0578 

508 

0586 

0595 

0603 

0612 

0621 

0629 

0638 

0646 

0655 

0663 

509 

0672 

0680 

0689 

0697 

0706 

0714 

0723 

0731 

0740 

0749 

5ie 

0757 

0766 

0774 

0783 

0791 

0800 

0808 

~08l7 

0825 

0834 

511 

0842 

0851 

0859 

0868 

0876 

0885 

0893 

0902 

0910 

0919 

512 

0927 

0935 

0944 

0952 

0961 

0969 

0978 

0986 

0995 

1003 

513 

1012 

1020 

1029 

1037 

1046 

1054 

1063 

1071 

1079 

1088 

514 

1096 

1105 

1113 

1122 

1130 

1139 

1147 

1155 

1164 

1172 

515 

1181 

1189 

1198 

1206 

1214 

1223 

1231 

1240 

1248 

1257 

516 

1265 

1273 

1282 

1290 

1299 

1307 

1315 

1324 

1332 

1341 

517 

1349 

1357 

1366 

1374 

1383 

1391 

1399 

1408 

1416 

1425 

518 

1433 

.  1441 

1450 

1458 

1466 

1475 

1483 

1492 

1500 

1509 

519 

1517 

1525 

1533 

1542 

1550 

1559 

1567 

1575 

1584 

1592 

vo. 

0 

1 

2 

3 

4  \ 

5 

6 

7 

8 

9 

A  TABLE  OP  LOGARITHMS. 


No.  5200—5800.                Log.  7160(5^76343^" 

NO.   0    1  ;  2 

3 

4 

5  |  6 

7 

8 

9 

520716007160971617 

71625 

71634 

7164271650 

71659 

71667 

71675 

521  \  1684  1692 

1700 

1709 

1717 

1725 

1734 

1742 

1750 

1759 

522j  1767 

1775 

1784 

1792 

1800 

1809 

1817 

1825 

1834 

1842 

523!  1850 

1858 

1867 

1875 

1883 

1892 

1900 

1908 

1917 

1925 

524 

1933 

1941 

1950 

1958 

1966 

1975 

1983 

1991 

1999 

2008 

525 

2016 

2024 

2032 

2041 

2049 

2057 

2066 

2074 

2082 

2090 

526 

2099 

2107 

2115!  2123 

2132 

2140 

2148 

2156 

2165 

2173 

527 

2181 

2189 

2198!  2206 

2214 

2222 

2230 

2239 

2247 

2255 

528 

2263 

2272 

2280!  2288 

2296 

2304 

2313 

2321 

2329 

2337 

529 

2346 

2354 

2362  2370 

2378 

2387]  23951  2403 

2411 

2419 

,530 

2428 

"2436 

2444j~2452 

2460 

2469  2477  2485 

2493 

~250l 

531 

2509 

2518 

2526;  2534 

2542  2550]  25581  2567 

2575 

2583 

532 

2591 

2599 

2607 

2616 

2624  2632  2640:  2648 

2656 

2665 

533 

2673 

2681 

2689 

2697 

2705  2713  2722;  2730 

2738 

2746 

534 

2754 

2762 

2770j  2779 

2787  2795  2803  2811 

2819 

2827 

535 

2835  2843 

2852  2860 

2868i  2876|  28841  2892 

2900 

2908 

536 

2916  2925 

2933 

2941 

2949 

2957  2965  2973 

2981 

2989 

537 

2997 

3006 

3014 

3022 

3030 

3038 

3046  3054 

3062 

3070 

538  3078 

3086 

3094  3102 

31111  3119 

3127  3135 

3143 

3151 

539|  3159 

3167 

3175]  3183 

3191 

3199!  3207)  3215 

3223 

3231 

5401  3239 

3247 

3"255i~3263 

"3272!  3280^  3288  ;  3~296 

3304 

3312 

541  3320 

3328 

3336  3344 

3352 

3360 

3368  3376 

3384 

3392 

542  3400 

3408 

3416  3424 

3432 

3440 

3448 

3456 

3464 

3472 

543  3480 

3488 

3496;  3504 

3512  3520!  3528 

3536 

3544 

3552 

544 

3560 

3568 

3576|  3584 

3592  3600!  3608 

3616 

3624 

3632 

545 

3640 

3648 

3656  3664 

3672  3679  3687 

3695 

3703 

3711 

546 

3719 

3727 

3735  3743 

3751  !  3759 

3767 

3775 

3783 

3791 

547 

3799 

3807 

3815  3823 

3830  S838 

3846 

3854 

3862 

3870 

548 

3878 

3886 

3894J  3902 

39101  3918 

3926 

3933 

3941 

3949 

549]  3957 

396*5 

3973!  3981 

3989  3997 

4005 

4013 

4020 

4028 

550~4036 

4044 

4052  4060 

4068  4076 

4084 

4092 

4099 

~4107 

551 

4115 

4123 

4131 

4139 

4147 

4155 

4162 

4170 

4178 

4186 

552 

4194 

4202 

4210 

4218 

4225 

4233 

4241 

4249 

4257 

4265 

553 

4273 

4280 

4288 

4296 

4304  4312 

4320 

4327 

4335 

4343 

554 

4351 

4359 

4367 

4374 

4382]  4390 

4398 

4406 

4414 

4421 

555 

4429 

4437 

4445 

4453 

4461 

4468 

4476 

4484 

4492 

4500 

5561  4507 

4515 

4523 

4531 

4539 

4547 

4554  4562 

4570 

4578 

557 

4586 

4593 

4601 

4609 

4617 

4624 

4632  4640 

4648 

4656 

558 

4663 

4671 

4679  4687 

4695 

4702 

4710  4718 

4726 

4733 

569 

4741 

4749 

4757  i  4764 

4772 

4780 

4788  4796 

4803 

4811 

560 

~48l9 

"4827 

4834 

4842 

4850  4858 

48651  4873 

It88l 

"4889 

561 

4896 

4904 

4912 

4920 

4927  4935 

4943  4950 

4958 

4966 

.562 

4974 

4981 

4989 

4997 

5005 

5012 

5020 

5028 

5035 

5043 

563 

5051 

5059 

5066 

5074 

5082 

5089 

5097 

5105 

5113 

5120 

564 

5128 

5136 

5143 

5151 

5159 

5166 

5174 

5182 

5189 

5197 

565 

5205 

5213 

5220 

5228 

5236 

5243 

5251 

6259 

5266 

5274 

.366 

5282 

5289 

5297 

5305 

5312 

5320 

6328  5335 

5343 

5351 

567 

5358 

5366 

5374 

5381 

5389 

5397 

5404  5412 

5420 

5427 

668 

5435 

5442 

54501  5458 

5465 

5473 

5481 

5488 

5496 

5504 

569 

5511 

5519 

5526J  5534 

5542 

5549 

5557 

5565 

5572 

5580 

570 

5587 

5595 

5603 

5610 

5618 

5626 

5633 

5641 

5648 

5656 

571 

5664 

5671 

5679 

5686 

5694 

5702 

5709 

5717 

5724 

5732 

572 

5740 

5747 

5755 

5762 

5770 

5778 

5785 

6793 

5800 

5808 

573 

5815 

5823 

5831 

5838 

5846 

5853 

5861 

5868 

5876 

5884 

574 

5891 

5899 

5906  5914 

5921 

5929 

5937 

5944 

5952 

5959 

575 

5967 

5974 

5982 

5989 

5997 

6005 

6012 

6020 

6027 

6035 

576 

6042 

6050 

6057 

6065 

6072 

6060 

6087 

6095 

6103 

6110 

577 

6118 

6125 

6133 

6140 

6148 

6155 

6163 

6170 

6178 

6185 

578 

6193 

6200 

6208 

6215 

6223 

6230 

6238 

6245 

6253 

6260 

579 

6268 

6275 

6283 

6290 

6298 

6305 

6313 

6320 

6328 

6335 

NO. 

0 

J 

2 

3  1  4 

~5~~ 

~6~ 

7 

8 

9 

14 


A  TABLE  OF  LOGARITHMS. 


N».  5800—6466.                 Log.  7^343—80618. 

NO.I  0 

1 

2 

3 

4 

5 

6 

7 

8    9 

560 

76343 

76350 

76358 

76365 

76373 

76380 

76388 

76395 

76403  76410 

581 

6418 

6425 

6433 

6440 

6448 

6455 

6462 

6470 

6477 

6485 

582 

6492 

6500 

6507 

6515 

6522 

6530 

6537 

6545 

6552 

6559 

583 

6567 

6574 

6582 

6589 

6597 

6604 

6612 

6619 

6626 

6634 

584 

6641 

6649 

6656 

6664 

6671 

6678 

6686 

6693 

6701 

6708 

585 

6716 

6723 

6730 

6738 

6745 

6753 

6760 

6768 

6775 

6782 

586 

6790 

6797  6805 

6812 

6819 

6827 

6834 

6842 

6849 

6856 

587 

6864 

6871 

6879 

6886 

6893 

6901 

6908 

6916 

6923 

6930 

588 

6938 

6945 

6953 

6960 

6967 

6975 

6982 

6989 

6997 

7004 

589 

7012 

7019 

7026 

7034 

7041 

7048 

7056 

7063 

7070 

7078 

590 

7085 

1093 

7100 

7107 

7115 

7122 

7129 

7137 

7144 

~7l51 

591 

7159 

7166 

7173 

7181 

7188 

7195 

7203 

7210 

7217 

7225 

592 

7232 

7240 

7247 

7254 

7262 

7269 

7276 

7283 

7291 

7298 

593 

7305 

7313 

7320 

7327 

7335 

7342 

7349 

7357 

7364 

7371 

594 

7379 

7386 

7393 

7401 

7408 

7415 

7422 

7430 

7437 

7444 

595 

7452 

7459 

7466 

7474 

7481 

7488 

7495 

7503 

7510 

7517 

596 

7525 

7532 

7539 

7546 

7554 

7661 

7568 

7576 

7583 

7590 

597 

7597 

7605 

7612 

7619 

7627 

7634 

7641 

7648 

7656 

7663 

598 

7670 

7677 

7685 

7692 

7699 

7706 

7714 

7721 

7728 

7735 

599 

7743 

7750 

7757 

7764 

7772 

7779 

7786 

7793 

7801 

7808 

600 

~78l5 

7822 

7830 

7837 

7844 

7861 

7859 

^7866 

"7873 

7880 

601 

7887 

7895 

7902 

7909 

7916 

7924 

7931 

7938 

7945 

7952 

602 

7960 

7967 

7974 

7981 

7988 

7996 

8003 

8010 

8017 

8025 

603 

8032 

8039 

8046 

8053 

8061 

8068 

8075 

8082 

8089 

8097 

604 

8104 

8111 

8118 

8125 

8132 

8140 

8147 

8154 

8161 

8168 

605 

8176 

8183 

8190 

8197 

8204 

8211 

8219 

8226 

8233 

8240 

606 

8247 

8254 

8262 

8269 

8276 

8283 

8290 

8297 

8305 

8312 

607 

8319 

8326 

8333 

8340 

8347 

8355 

8362 

8369 

8376 

8383 

608 

8390 

8398 

8405 

8412 

8419 

8426 

8433 

8440 

8447 

8455 

609 

8462 

8469 

8476 

8483 

8490 

8497 

8504 

8512 

8519 

8526. 

610 

8533 

8540 

8547 

8554 

8561 

8569 

8576 

8583 

8590 

8597 

611 

8604 

8611 

8618 

8625 

8633 

8640 

8647 

8654 

8661 

8668 

612 

8675 

8682 

8689 

8696 

8704 

8711 

8718 

8725 

8732 

8739 

613 

8746 

8753 

8760 

8767 

8774 

8781 

8789 

8796 

8803 

8810 

614 

8817 

8824 

8831 

8838 

8845 

8852 

8859 

8866 

8873 

8880 

615 

8888 

8895 

8902 

8909 

8916 

8923 

8930 

8937 

8944 

8951 

616 

8958 

8965 

8972 

8979 

8986 

8993 

9000 

9007 

9014 

9021 

617 

9029 

9036 

9043 

9050 

9057 

9064 

9071 

9078 

9085 

9092 

618 

9099 

9106 

9113 

9120 

9127 

9134 

9141 

9148 

9155 

9162 

619 

9169 

9176 

9183 

9190 

9197 

9204 

9211 

9218 

9225 

9232 

6iO 

9239 

9246 

9253 

9260  9267 

9274 

9281 

9288 

9295 

9302 

621 

9309 

9316 

9323 

9330 

9337  9344 

9351 

9358 

9365 

9372 

622 

9379 

9386 

9393 

9400 

9407  9414 

9421 

9428 

9435 

9442 

623 

9449 

9456 

9463 

9470 

9477  9484 

9491 

9498 

9505 

9511 

624 

9518 

9525 

9532  9539 

9546  9553 

9560 

9567 

9574 

9581 

625 

9588 

9595 

9602 

9609 

9616  9623 

9630 

9637 

9641 

9650 

626 

9657 

9664 

9671 

9678 

9685!  9692 

9699 

9706 

9713 

9720 

627 

9727 

9734 

9741 

9748 

9754  9761 

9768 

9775 

9782 

9789 

628 

9796 

9803 

9810 

9817 

9824J  9831 

9837 

9844 

9851 

9858 

629 

9865 

9872 

9879 

9886 

9893!  9900 

9906 

9913 

9920 

9927 

630 

9934 

9941 

9948 

9955 

9962  9969 

9975|  9982 

9989 

9996 

631 

80003 

80010 

80017 

80024 

60030:80037 

80044 

80051 

80058 

80065 

632 

0072 

0079 

0085 

0092 

0099 

0106 

0113 

0120 

0127 

0134 

633 

0140 

0147 

0154 

0161 

0168 

0175 

0182 

0188 

0195 

0202 

634 

02Q9 

0216 

0223 

0229 

0236 

0243 

0250 

0257 

0264 

0271 

635 

0277 

.0284 

0291 

0298 

0305 

0312 

0318 

0825 

0332 

0339 

0346 

0353 

0359 

0366 

0373 

0380 

0387 

0393 

0400 

0407 

637 

0414 

0421 

0428 

0434 

0441 

0448 

0455 

0462 

0468 

0475 

638 

0482 

0489 

0496 

0502 

0509 

0516 

0523 

0530 

0536 

0543 

639 

0550 

0557 

0564 

0570 

0577 

0584 

0591 

0598 

0604 
___ 

0611 
__ 

NO 

0 

1 

2 

3 

4 

5 

6 

7 

A  TABLE  OF  LOGARITHMS. 


15 


No.  6400—7006.                 Log.  80618—84610. 

NO. 

0    1  j  I 

i 

4 

5 

6 

7 

8    9 

40 

B0618j80625i80632 
06861  0693  0699 

80638 
0766 

3064580662 
0713'  0720 

"0659!80665 
0726  0733 

80672  80679 
0740  0747 

42 

07541  0760J  0767 

0774 

0781|  0787 

0794  0801 

0808  0814 

643 

0821  0828  0835 

0841 

0848,  0855 

0862  0869 

0675  0882 

644 

0889  0895 

0902 

0909 

09161  0922 

09291  0936 

0943 

0949 

645 

0956  0963 

0969 

0976 

0983  0990 

0996  1003 

1010 

1017 

646 

1023  1030 

1037 

1043 

1050  1057 

1064  1070 

1077 

1084 

647 

1090  1097 

1104 

1111 

1117  1124 

1131 

1137 

1144 

1151 

648 

1158 

1164 

1171 

1178  11841  1191 

1198  1204 

1211 

1218 

649 

1224 

1231 

1238 

1245 

1251!  1258 

1265  1271 

1278 

1285 

650 

1291 

1298 

1305 

1311 

1318  1325 

1331!  1338 

1345 

1351 

651 

1358 

1365 

1371 

1378 

1385 

1391 

1398  1405 

1411 

1418 

652 

1425 

1431 

1438 

1445 

1451 

1458 

1465  1471 

1478 

1485 

653 

1491 

1498 

1505 

1511 

1518 

1525 

153l!  1538 

1544 

1551 

654 

1558 

1564 

1571 

1578 

1581 

1591 

1598  1604 

1611 

1617 

655 

1624 

1631 

1637 

1644 

1651 

1657 

1664 

1671 

1677 

1684 

656 

16901  1697 

1704 

1710 

1717 

1723 

1730!  1737 

1743 

1750 

657 

1757  1763 

1770 

1776 

1783 

1790 

17961  1803 

1809 

1816 

658 

1823 

1829 

1836 

1842 

1849  1856 

186-2  1869 

1875 

1882 

659 

1889 

1895 

1902 

1908 

1915  1921 

1928  1935 

1941 

1948 

660 

"1954 

1961 

1968 

1974 

1981  1987 

1994  2000 

2007 

2014 

661 

2020 

2027 

2033 

2040 

2046  2053 

2060  2066 

2073  2079 

662 

2086 

2092 

2099 

2105 

2112  2119 

2125 

2132 

2138  2145 

663 

2151 

2158 

2164 

2171 

2178|  2184 

2191 

2197 

2204  2210 

664 

2217 

2223 

2230 

2236 

22431  2249 

2256 

2263 

2269 

2276 

665 

2282 

2289 

2295 

2302 

2308!  2315 

2321 

2328 

2334 

2341 

666 

2347:  2354 

2360 

2367 

2373  2380 

2387 

2393 

2400 

2406 

667 

2426 

2432 

2439  2445 

2452 

2458 

2465 

2471 

668  2478!  2484 

2491 

2497 

2504'  2510 

2517 

2523 

2530 

2536 

6691  2543 

2549 

2556 

2562 

2569  2575 

2582 

2588 

2595 

2601 

670  2607 

2614 

2620 

2627 

2633 

2640 

2646 

2653 

2659 

2666 

671 

2672 

2679 

2685 

2692 

2698 

2705 

2711 

2718 

2724 

2730 

672 

2737 

2743 

2750 

2766 

27631  2769 

2776 

2782 

2789 

2795 

673 

2802 

2808 

2814 

2821 

28271  2834 

2840 

2847 

2853 

2860 

674 

2866 

2872 

2879 

2885 

2892  2898 

2905 

2911 

2918 

2924 

675 

2930 

2937 

2943 

2950 

2956 

2963 

2969 

2976 

2982 

2988 

676 

2995 

3001 

3008 

3014 

3020 

3027 

3033 

3040 

3046 

3052 

677 

3059 

3065 

3072 

3078 

3085 

309 

3097 

3104 

3110 

3117 

678 

3123 

3129  3136 

3142:  3149 

3155  3161 

3168 

3174 

3181 

679 

3187 

3193  3200 

3206!  3213  3219*  3225 

3232 

3238 

3245 

680 

3251 

3257  3264 

3270  3276  3283  3289 

3296 

3302 

"3308 

681 

3315 

3321  3327 

3334  3340  3347  3353 

3359 

3366 

3372 

682 

3378 

3385  3391 

3398  3404  3410!  3417 

3423 

3429 

3436 

683 

3442 

3448  3455 

3461  3467  3474J  3480 

3487 

3493 

3499 

684 

3506 

3512  3518 

3525  3581  3537  3544 

3550 

3556 

3563 

685 

3569 

3575  3582 

3588  3594,  3601  3607 

3613 

3620 

3626 

686 

3632 

3639  3645 

365V  3658  3664  3670 

3677 

3683 

3689' 

687 

3696 

3702  3708 

3716  3721|  3727i  3734 

3740 

3746 

3753 

688 

3759 

37651  3771 

3778)  3784  3790:  3797 

3803 

3809 

3816 

689 

3822 

3828  3835 

3841  3847  3853,  3860 

3866 

3872 

3879 

690 
691 

3885 
3948 

3891  '  3897 
3954  3960 

3904  39101  3916J  3923 
3967  39731  3979!  3985 

3929 
3992 

3935 
3998 

394ii 
4004 

692 

4011 

4017  4023 

4029  4036 

40421  4048 

4055 

4061 

4067 

693 

4073 

4080  4086 

4092 

4098 

4105  4111 

4117 

4123 

4130 

694 

4136 

4142J  4148 

4155  4161 

4167  4173 

4180 

4186 

4192 

695 

4198 

4205;  4211 

4217  4223 

4230  4236 

4242 

4248 

4255 

696 

4261 

42671  4273 

4280J  4286 

4292  4298 

4305 

4311 

4317 

697 

4323 

4330  4336 

4342 

4348 

4354  4361 

4367 

4373 

4379 

698 

4386 

4392  4398 

4404 

4410 

4417)  4423 

4429 

4435 

4442 

699 

4443 

4454]  4460 

4466  4473 

4479)  4485 

4491 

4497 

4504 

\-Q. 

0 

1 

3 

3  |  4 

5  1  6 

7 

8 

9 

16 


A  TABLE  OF  LOGARITHMS. 


N6T7000  —  7600. 

JLog.  84510  —  38081. 

NO.   0 

1 

2 

s 

4    5 

6 

7 

8    9 

700  84510  84518!84522  84528  84535  84541  84547  84553  84559  84566 

701  4572)  4578 

4584 

4590 

4597  4603  460d 

4615  4621  4628 

702  4634J  4640 

4646 

4652 

4658  4665  4671 

4677  4683  4689 

703  46961  4702 

4708 

4714 

4720  4726  4733  4739  4745  4751 

704  4757  4763 

4770 

4776 

4782  4788 

4.794  4800  4807  4813 

705  4819  4825 

4831 

4837 

4844  4850  4856 

4862  4868;  4874 

706  4880  4887 

4893 

4899 

4905;  4911 

4917 

4924 

4930 

4936 

7071  4942!  4948 

4954 

4960 

4967 

4973 

4979 

4985  4991 

4997 

708:  5003!  5009 

5016 

5022 

5028 

5034 

5040  5046-  5052 

5058 

709;  50651  5071J  5077 

5083 

5089 

5095 

5101 

5107 

5114 

5120 

710i  5126  5132J  5138 

5144 

5150 

~6l56 

5163 

5169 

5175 

5181 

711  5187 

5193 

5199 

5205 

5211 

5217 

5224  5230  6236 

5242 

712 

5248 

5254 

5260 

5266 

5272 

5278 

5285 

:  5291 

5297 

5303 

713 

5309 

5315 

5321 

5327 

5333 

5339 

5345 

5352 

5358 

5364 

714 

5370 

5376 

5382 

5388 

5394 

5400 

5406 

5412 

5418 

5425 

715 

5431 

5437 

5443 

5449 

5455 

5461 

5467 

5473 

5479 

5485 

716 

5491 

5497 

5503 

5509 

5516 

6622 

5528 

5534 

6540 

5546 

717 

5552 

5558 

5564 

5570 

6576 

5582 

5588 

5594 

,  5600 

5606 

718 

5612 

5618 

5625 

5631 

5637  5643 

6649 

5655 

5661  6667 

719 

5673 

5679 

6685 

5691 

5697  5703 

5709 

5715 

5721  5727 

720 

5733 

5739 

5745 

5751 

5757  5763 

5769 

6776 

5781  5788 

721 

5794 

5800 

5806 

5812 

5818  5824 

5830 

5836 

5842  5848, 

722 

5854 

5860 

5866 

5872 

58781  5884 

5890 

5896 

5902:  5908 

723 

5914 

5920 

5926 

5932 

5938  5944 

5950 

5956  5962  5968 

724 

5974 

5980 

5986 

5992 

5998!  6004 

6010 

6016  6022,  6028 

725 

6034 

6040 

6046 

6052 

6058!  6064 

6070 

6076J  6082  6088 

726 

6094 

6100 

6106 

6112 

6118:  6124 

6130 

6136 

6141  6147 

727 

6153 

6159 

6165 

6171 

6177i  6183 

6189 

6195 

6201  6207 

728 

6213 

6219 

6225 

6231 

6237J  6243 

6249 

6255 

6261  6267 

729 

6273 

6279 

6285 

6291 

6297!  6303 

6308 

6314 

6320;  6326 

730 

6332 

6338 

~6344 

6350  6356J  6362  6368 

6374 

6380!  6386 

731 

6392 

6398 

6404 

6410 

64151  6421 

6427 

6433 

6439  6445 

732 

6451 

6457 

6463 

6469 

6475  6481 

6487 

6493 

6499  6504 

733 

6510  6516 

6522 

6528 

6534  6540 

6546 

6552 

6558,  6564 

734 

6570!  6576 

6581 

6587 

65931  6599 

6605 

6611 

6617;  6623 

735 

6629 

6635 

6641 

6646 

6652  6658 

6664 

6670 

6676  6682 

736 

6688 

6694 

6700!  6705 

6711  6717 

6723 

6729 

6735  1  6741 

737 

6747 

6753 

6759 

6764 

6770  6776 

6782 

6788 

6794,  6800 

738 

6806 

6812 

6817  6823 

6829  6835 

6841 

6847 

6853  6859 

739 

6864 

6870:  6876  6882  6888  6894 

6900 

6906 

6911  6917 

740 

6923 

6929  6935 

6941 

6947  6953 

6958 

6964 

~6970  6976 

741 

6982  6988 

6994 

6999 

7005  7011 

7017 

7023 

7029  7035 

742 

7040  7046!  7052 

7058 

7064 

7070 

7075 

7081 

7087 

7093 

743 

7099 

7105 

7111 

7116 

7122 

7128 

7134 

7140 

714*3  71511 

744 

7157 

7163 

7169 

7175 

7181  7186!  7192 

7198 

72041  7210  ! 

745  72161  7221 

7227 

7233 

7239;  7245 

7251 

7256 

7262  7263! 

746  7274!  7280 

7286 

7291 

72971  7303  7309 

7315 

7320  7326 

747  7332!  7338 

7344 

7349 

7365 

7361 

7367'  7373 

7379 

7384 

748J  7390 

7396 

7402 

7408 

7413 

7419  74251  7431 

7437 

7442 

749  7448 

7454 

7460 

7466 

7471 

7477 

7483|  7489 

7495 

7500 

750  7506 

7512 

7518 

7523 

7529 

7535 

75411  7547 

7552 

7558 

751  7564 

7570|  7576 

7581 

7587  7593  7599!  7604 

7610 

7616 

752  7622 

7628!  7633 

7639 

7645  7651 

7656  7662 

7668 

7674 

753  7679 

7685J  7691 

7697 

7703  7708  7714 

7720 

7726 

7731 

754  7737 

7743 

7749 

7754 

7760 

7766  7772 

7777 

7783 

7789 

765t  7795 

7800 

7806 

7812 

7818 

7823 

7829 

7835 

7841 

7846, 

756  7852 

7858 

7864 

7869 

7875 

7881 

7887 

7892 

7898 

7904 

767  7910 

7915 

7921 

7927 

7933 

7938 

7944 

7950 

7955 

7961 

758  7967 

7973 

7978 

7984 

7990 

7996 

8001 

8007 

8013 

8018 

Y59  8024 

8030 

8036 

8041 

8047 

8053 

8058 

8064 

8070 

8076 

ko.  0 

1 

2 

3 

4 

,  6 

6 

7 

8 

9 

A  TABLE  OF  LOGARITHMS. 


No.  7600—  820Q. 

Log 

88081—91381. 

NO.!   0 

1 

2 

3  1 

4  i  5  ! 

«J 

7  |  8 

9 

76088081 
761'  8138 

88087* 

8144; 

sossi 

8150 

38098 
8156 

38104881108 
8161,  8167i 

18160 
81731 

38121  |88I27 

8178!  8184 

38133 
8190 

762!  8195 

8201! 

8207 

8213 

8218-  8224 

8230 

82351  8241 

8247 

763  8252 

8258; 

8264 

82701 

8275>  8281 

8287 

8292:  8298 

8304 

7£4  8309 

8315' 

832L 

8326; 

8332  S338 

8343 

8349!  8355 

8360 

765  8366 

8372 

8377 

8383 

8389  83951 

84001 

8406'i  8412 

8417 

766  8423 

8429 

8434! 

8440! 

8446  84511 

8457; 

84631  84681 

8474 

767  8480 

8485 

84911 

8497 

8502  8508 

8513 

8519!  85251 

8530 

768  8536 

8542 

8547 

8553 

8559!  85641 

8570 

8576  858l! 

8587 

769  8593 

8598 

8604 

8610 

8615:  8621' 

862? 

8632  8638 

8643 

770  8649 

~8665f 

86601 

"86(56 

8672  8677 

"8683 

8689  i  8694,  "8700 

771  8705 

8711 

8717! 

8722, 

8728  8734 

8739 

8745  8750 

8756 

772  8762 

8767 

8773 

8779, 

8784  8790! 

8795 

8801  8807 

8812 

773  8818 

8824, 

8829 

8835 

8840  8846 

8852 

8857  8863 

8868 

774  8874 

8880 

8885: 

8891 

8897  8902 

8908 

8913  8919 

8925 

775  8930 

8936 

8941; 

8947 

8953  8958 

8964 

8969  8975 

8981 

776  8986 

8992: 

8997 

9003 

9009  9014 

9020 

9025  9031 

9037 

777  9042 

9048 

9053! 

9059 

9064  9070 

9076 

081  087 

092 

778  9098  9104  9109 

9115 

9120  9126 

9131 

137   143 

148 

779  9154 

9159| 

9165 

9170 

9176  9182 

9187J  193  198 

204 

780  9209 

9215 

922  L 

9226 

~9232~9237 

9243 

248  254j  260 

781  9265 

927  1! 

9276 

9282 

9287  9293 

9298 

304  310  315 

782  9321 

93261 

9332 

9337 

9343  9348 

9354 

360  365 

371 

783  93761  9382 

9387 

9393 

9398  9404 

9409 

415  421|  426 

784  9432!  9437, 

9443 

9448 

9454  9459; 

9465 

470  476,  481 

785  9487 

9492; 

9498 

9504 

9509  9515; 

9520 

526  531 

537 

786  9542 

9548! 

9553 

9559'  9564  9570! 

9575 

581  586 

592 

787  9597 

9603 

9609 

9614 

9620  9625 

9631 

636  642  64 

788  9653 

9658 

9664 

9669 

9675  9680 

9686 

691  B97 

702 

789  9708 

9713! 

9719 

9724 

9730  9735 

9741 

746  752 

757 

790  9763  9768 

9774 

9779 

~9785  9790 

9796i~80i  807 

812 

791  9818  9823 

9829 

9834 

9840  9845 

9851J  856  862  867 

792  9873 

9878 

9883 

98S9 

9894  9900 

9905 

911  916;  922 

793  9927 

9933 

9938 

9944 

9949  9955 

9960 

966  971 

977 

794  9982 

9988 

9993 

9998  90004  90009  90015  90020  90026  90031 

795  90037  90042  90048  90053 

0059  0064 

0069 

0075  0080 

0086 

796  0091 

00971 

0102 

0108 

0113  0119 

0124 

0129  0135 

0140 

797  0146  0151  j 

0157 

0162 

0168  0173 

0179 

0184  0189 

0195 

798  0200!  0206 

0211 

0217 

0222  0227 

0233!  0238  0244 

0249 

799  0255  0260 

0266 

0271 

0276  0282 

0287 

i  0293  0298 

0304 

800  0309  0314 

0320 

0325 

0331  0336 

0342  0347  0352 

0358 

801  0363  0369 

0374 

0380 

0385  0390 

0396  0401  0407 

0412 

802  0417  0423 

0428 

0434 

0439  0445 

0450.  0455  0461 

0466 

803  0472  0477 

048-2 

0488 

0493  0499 

0504 

0509  0515 

0520 

804  0626  0531 

0536 

0542 

0547  0553 

0558;  0563  0569 

:  0574 

805  0580  0585 

0590 

0596 

0601  0607 

0612  0617  0623  0628 

806  0634  0639 

0644 

0650 

0655  0660 

0666  0671  0677 

0682 

807  06871  0693 

0698 

0703 

0709  0714 

0720  0725  0730!  0736 

808  0741  0747 

0752 

0757 

0763  0768 

0773  0779  i  0784 

i  07ft9 

809  0795  0800 

0806 

0811 

0816  0822 

0827!  0832J  0838;  0843 

810  0849  0854 

0859 

0865  0870  0875 

0881 

0886i  0891 

OR97 

811  0902'  0907 

0913 

0918  0924  0929  0934 

0940  0945  0950 

812  095( 

>  0961 

09661  0972  0977  0982:  098S 

0993!  0998 

1004 

813  100J 

)  1014 

1020 

1025,  1030  1036 

1041)  1046|  1052 

1057 

814  10621  1068 

1073J  1078J  1084  1089 

1094  1100,  1105 

1110 

815  1116!  1121 

1126|  11321  1137  1142 

1148i  1153  1158 

1164 

816  1169  1174 

118C 

11851  1190,  1196!  1201!  1206J  1212 

1217 

817  1222  1228 

1233 

1238  1243,  12491  12541  12591  1265 

1270 

818  1275  1281 

1286 

1291  1297  1302 

1307!  13121  1318 

1323 

819  1328(  1334 

133S 

1344 

1  1350  1355 

13tt 

)  1365)  1371 

1376 

NO.;  0 

"  l 

~2~|  3 

4  |  5  i  6  j~T~|~~8~ 

9 

18 


A  TABLE  OF  LOGARITHMS, 


No.  8200  —  88CO. 

Log.  91381—94448, 

NO 

0,1,2 

3 

4    5 

6 

7 

1  8" 

9 

82C 

91381  91387  91395 

5  91397  91403  91408!91413'91418  91424 

91429 

821 

1434  144( 

I44i 

>  1450 

1455  1461  1466 

1471!  1477 

1482 

822 

1487 

149* 

149* 

*  1503 

1508  1514]  1519 

1524 

1529 

1535 

823 

154C 

154i 

1551 

1556 

1561  15661  1572 

1577 

1582 

1587 

824 

1593 

159£ 

160£ 

1609 

1614  1619 

1624 

1630!  1635 

1640 

825 

1645 

15,31 

1656 

1661 

16661  1672 

1677 

1682 

1687 

1693 

826 

1691  1703 

1709!  1714 

1719  1724 

1730 

1735 

1740 

1745 

827 

1751  1756 

1761 

1766 

177S 

\  1777 

1782 

1787 

1793 

1798 

828 

1803 

1808  1814 

1819 

1824  1829 

1834 

1840 

1845 

1850 

829 

1855  1861 

1866J  1871 

1876  1882 

1887 

1892 

1897 

1903 

830 
831 

19081  1913  "1918 
1960  1965  1971 

1924 
1976 

1929  "1934 
1981  1986 

1939 
1991 

T944 
1997 

1950 

2002 

1955 

2007 

832 

2012  2018  2023 

2028 

2033  2038 

2044 

2049 

2054 

2059 

833 

2065 

2070  2975  2080 

2085  2091 

2096 

2101 

2106 

2111 

834 

2117 

2122 

2127  21321 

2137  2143 

2148 

2153 

2158 

2163 

835 

2169 

2174 

2179 

2I84| 

2189  2195 

22001 

22051 

2210 

2215 

836 

2221 

2226 

2231 

2236 

2241  2247 

2252: 

2257 

2262J 

2267 

837 

2273 

2278 

2283 

2288^ 

2293  2298 

2304 

2309 

2314! 

2319 

838 

2324 

2330 

2335 

23401 

2345  2350 

2355 

2361 

2366 

2371 

839 

2376 

2381 

2387 

2392; 

2397  2402 

2407 

2412 

2418: 

2423 

840 

2428 

!>433 

2438 

"2443 

2449  2454 

2459 

2464 

2469 

2474 

841 

2480 

2485 

2490  2495 

25001  2505 

2511 

2516 

2521 

2526 

842 

2531 

2536 

2542 

2547 

25521  2557 

2562 

2567 

2572 

2578 

843 

2583 

2588 

2593 

2598 

2603  2609 

2614 

2619 

2624 

2629 

844 

2634 

2639 

2645 

2650 

2655  2660 

2665 

2670 

2675 

2681 

845  2686  2691 

2696 

2701 

2706 

2711 

2716 

2722 

2727 

2732 

846  2737  2742 

2747 

2752 

2758 

2763 

2768 

2773 

2778 

2783 

847  27881  2793 

2799 

2804 

2809 

2814 

2819 

2824 

2829 

2834 

848!  2840  2845 

2850 

2855 

2860 

2865 

2870 

2875 

2881 

2886 

849|  2891 

2896 

2901 

2906 

2911 

2916 

2921 

2927 

2932 

2937 

850 

2942 

"2947 

2952 

2957" 

2962 

~2967l>973 

2978 

2983 

2988 

861 

2993 

2998 

3003 

3008 

3013 

3018 

3024 

3029 

3034 

3039 

852 

3044 

3049 

3054 

3059 

3064 

3069 

3075 

3080 

3085. 

3090 

853 

3095 

3100 

3105 

3110 

3115 

3120 

3125 

3131 

3136 

3141 

854 

3146  3151 

3156 

3161 

3166 

3171 

3176 

3181 

3186 

3192 

855 

31971  3202 

3207 

3212 

3217 

3222  i 

3227 

3232 

3237 

3242 

856 

3247]  3252 

3258 

3263 

3268 

3273 

3278 

5283 

3288 

3293 

857 

3298.  3303 

3308 

3313 

3318 

3323 

3328 

3334 

3339 

3344 

8581  33491  3354 

3359 

3364 

3369 

3374 

3379 

3384 

3389 

3394 

859)  3399  3404 

3409 

3414 

3420 

3425 

3430 

3435 

3440 

3445 

860,  3450  3455 

3460 

3465" 

3470 

3475 

3480 

3485 

3490 

3495 

86  li  3500  3505 

3510 

3515 

3520 

3526 

3531 

3536 

3541 

3546 

862  3551  i  3556 

3561 

3566 

3571 

3576 

3581 

3586 

3591 

3596 

8631  3601  3606 

3611 

3616 

3621 

3626; 

3631 

3636 

3641 

3646 

8641  3651  i  3656 

3661 

3666 

3671  !  3676! 

3C82 

3687 

3692 

3697 

865|  37,02  3707 

3712 

3717 

3722J  3727' 

3732 

3737 

3742 

3747 

866  3752  3757 

3762 

3767 

3772  3777! 

3782 

3787. 

3792" 

3797 

867!  3802J  3807 

3812 

3817 

3822J  3827! 

3832 

3837; 

3842 

3847 

868  3852  3857  3862 

3867 

3872,  3877 

3882 

38871 

3892' 

3897 

869  3902  3907  3912 

3917, 

3922J  3927 

3932 

3937 

3942, 

3947 

870  3952-  "3957  "3962 

"3967  " 

3972!  3977" 

3982  3987; 

3992:' 

"3997 

871  4002  4007  4012 

4017 

4022  4027i 

4032 

4037  • 

4042 

4047 

872  4052;  4057  4062 

4067 

4072 

4077 

4082: 

4086; 

4091| 

4096 

873  4101  4106  4111 

4116 

4121 

4126 

4131 

4136 

4141 

4146 

874  4151  4156  4161 

4166, 

4171 

4176J 

4181 

4186' 

4191 

4196 

875  4201  4206  4211 

42161 

4221 

4226J 

4231 

42361 

4240! 

4245 

876:  4250  4255;  4260 

4265, 

4270 

4275! 

4280 

4285i 

4290 

4295 

8771  4300  4305!  4310 

4315 

4320 

4325 

4330 

43351 

4340: 

4345 

8781  4349  4354  4359 

4364J 

4369 

4374 

4379 

4384! 

43891 

4394 

879i  4399  4404  4409 

4414 

4419 

4424 

4429 

4433; 

4438! 

4443 

NO.;  0,1(2 

3  | 

4 

5  j 

6  i 

7  i 

~8~| 

9 

A  TABLE  OP  LOGARITHMS, 


"No.  8800^-9400. 

Log.  9444 

3—  97.. 
8 

113. 

NO. 

0 

1 

2 

3 

4 

5 

b  |  7 

-L. 

880 

94448 

94453 

94458 

94463 

94468 

94473 

9447894483 

94488194493 

881 

4498 

4503 

4507 

4512 

4517 

4522 

4527J  4532 

4537J  4542 

882 

4547 

4552 

4557 

4962 

4567 

4571 

4576!  4581 

4586  4591 

883 

4596 

4601 

4606 

4611 

4616 

4621 

4626'  4630 

46351  4640 

884 

4645 

4650 

4655 

4660 

4665 

4670 

4675  4680 

4685 

4689 

885 

4694 

4699 

4704 

4709 

4714 

4719 

4724  4729 

4734 

4738 

886 

4743 

4748 

4753 

4758 

4763  4768 

4773  4778 

4783 

4787 

887 

4792 

4797 

4802 

4807 

4812  4817! 

4822  4827 

4832 

4836 

888 

4841 

4846 

4851 

4856 

4861 

4866| 

4871  4876 

4880!  4885 

889 

4890 

4895 

4900 

4905 

4910 

4915 

4919  4924 

49291  4934 

890 

4939 

4944  4949 

4954 

4959  4963' 

4968  4973 

4978 

4983 

891 

4988 

4993  4998 

5002 

5007 

5012! 

5017  5022 

5027 

5032 

89-2 

5036 

5041  5046 

5051 

5056 

5061 

5066  5071 

5075 

5080 

893 

5085 

5090  5095 

5100 

5105 

5109 

5114  5119 

5124 

5129 

894 

5134 

5139  5143 

5148 

5153 

5158 

5163  5168 

51731  5177 

895 

5182 

5187)  5192 

5197 

5202 

5207 

5211  5218J  5221 

!  5226 

896 

5231 

5236 

5240 

5245 

5250 

5255 

5260  5265!  5270',  5274 

897 

5279 

5284 

5289 

5294 

5299 

5303 

5308  5313 

5318!  5323 

898 

5328 

5332  5337 

5342 

5347 

5352 

5357  5361 

5366  5371 

899 

5376 

5381  5386 

5390  5395 

5400 

5405  5410;  64151  -5419 

900 

5424 

5429 

5434 

^4391  "5444 

5448 

5453  5458!  5463  5468 

901 

5472 

5477 

5482 

54871  5492 

5497 

5501  5506  5511 

5516 

902 

5521 

5525 

5530 

5535  5540 

5545 

5550  5554  5559  5564 

903 

5569 

5574  5578 

55831  5588 

5593 

5598  56021  5607  5612 

904 

5617 

5622 

5626 

5631 

5636 

5641 

5646  5650  5655  5660 

905 

5665 

5670 

5674 

5679  5684 

5689 

5694  6698  5703  5708 

906 

5713 

5718 

5722 

5727  5732 

5737 

5742  5746  5751  5756 

907 

5761 

5766 

5770 

57751  5780 

5785 

5789  5794  5799  5804 

908 

5809 

5813 

5818  5823 

5828  5832 

5837  5842  5847  5852 

909 

5856 

5861 

5866  5871 

5875  5880 

5885  5890  5895  5899 

910 

5904 

5909 

5914 

59181  5923  5928 

5933  5938  5942  594 

911 

5952 

5957 

5961 

5966 

5971 

5976 

5980  5985  599( 

)  5995 

912 

5999 

6004!  6009 

6014i  6019 

6023 

6028  6033  6038  6042 

913 

6047 

6052;  6057 

6061 

!  6066 

6071 

6076  6080  6085  6090 

914 

6095 

6099  6104 

6109i  6114 

6118 

6123  6128  6133;  6137 

915 

6142 

6147  6152  6156 

6161 

6166 

6171  6175  6180  6185 

916 

6190 

6194  6199  6204 

6209 

6213 

6218  6223  6227  6232 

917 

6237 

6242;  6246  6251 

:  6256 

6261 

6265  627( 

)  6275  6280 

918  6284 

6289  6294!  6298  6303 

6308 

6313  6317  6322  6327 

919]  6332 

6336  6341  6346  6350 

6355 

6360  6365  6369  6374 

920  6379  6384  6388i  6393  6398 

6402 

6407  6412  6417  6421 

921  6426  6431  6435!  6440  6445!  6450  6454  6459  6464  646 

922  6473,  6478  6483  6487!  6492J  6497 

6501  6506  6511  6515 

923  6520  6525  6530  6534  6539;  6544  6548  6553  6558  656 

924  6567  6672  6577;  6581;  6586  ,  6591 

6596  6600  6605  6609 

925 

6614  6619  6624!  662? 

6633  6638  6642  6647  6652  6656 

926 

6661  6666  6670!  6675!  6680!  6685  6689  6694  669 

9  6703 

927  6708J  6713  6717J  6722|  6727!  6731 

6736  6741  6745  6750 

928  6755  6759  6764  6769  67741  6778  6783  6788  6792  6797 

929  6802  6806  681  Ij  6816  6820',  6825  6830  6834  683 

3  6844 

930  "6848,^5853  ~6858"!  6862  ~6867''-6872  ~6876  ~688l  ~68» 

5  6890 

931  6895  6900  C904l  6909  6914  6918  6923  6928  693 

I  6937 

932  6942  6946  6951  6956  6960  6965 

6970  6974  697 

9  6984 

933  6988  6993  6997:  7002;  7007  7011 

7016  7021  7025  7030 

934  7035  7039  7044  7049  j  7053i  705£ 

7063  7067  7072  7077 

935  7081  7086  7090  7095)  7100i  1104 

7109  7114  7118  7123 

936  7128  7132  7137  7142J  7146;  7151 

7155  7160  7165  7169 

937  7174  7179  7183  71881  7192'  7197 

7202  7206  7211  7216 

938  7220  7225  7230  7234  7239  7243 

7248  7253  7257  7262 

939  7267  7271  7276  7280  7285i  729C 

7294  7299  7304J  7308 

Sol,  0  i  1    2    3 

—  i— 

—  |  — 

"I"5" 

1  9 

A  TABLE  OF  LOGARITHMS. 


~~Nb.  94bo—  iSCob. 

L*og.  97313  —  99996. 

NO.  0 

1  , 

213    4 

5  1 

g-  ~  Tj  - 

8 

9 

940  97313  97317  97322  97327  97331  97336  97340  97345  97350  97354 

941  7359 

7364! 

7368  7373'  7377  7382! 

7387  7391 

7396 

7400 

942  7405, 

7410 

7414!  7419  7424 

7428i 

7433  7437 

7442 

7447 

943  7451 

7456 

7460!  7465  7470 

7474! 

7479  7483 

7488 

7493 

944  7497 

7502 

7506j  7511  7516 

7520[ 

7525  7529 

7534 

7539 

945  7543 

7548 

7552  7557i  7562 

7566i 

7571  7575 

7580! 

7585 

946  7589 

7594 

7598i  7603!  7607 

7612 

7617  7621 

7626| 

7630 

947  7635 

7640 

7644'  76491  7653 

7658 

7663  7667 

7672 

7676 

948  7681 

7685 

7690i  7695i  76.99 

7704 

7708  7713 

7717 

7722 

949  7727 

7731 

7736!  7740;  7745 

7749; 

7754  7759 

7763 

7768 

950  7772" 

7777" 

7782~T786  7791  "7795  " 

7800  7804 

7809 

7813 

951  7818 

7823 

7827  7832  7836 

7841 

7845  7850 

7855; 

7859 

952  7864 

7868 

7873,  7877  7882 

7886 

7891  7896 

7900 

7905 

953  7909 

7914 

7918  7923  7928 

7932 

7937  7941 

7946 

7950 

954  7955 

7950 

7964  79681  7973 

7978 

7982  7987 

7991 

7996 

955  8000 

8005 

8009  8014  8019 

8023 

8028  8032 

8037 

8041 

956  8046; 

8050 

8055  8059 

8064 

8068 

8073  8078 

8082, 

8087 

957  8091 

8096 

8100  8105 

8109 

8114 

8118  8123 

8127 

8132 

958  8137: 

8141 

8146  8150|  8155 

8159 

8164  8168 

8173 

8177 

959  8182j 

8186 

8191  8195;  8200 

8204 

8209  8214 

8218 

8223 

960  82271" 

8232  " 

8236  "82411  8245  " 

8250, 

8254  8259" 

8263 

8268 

961  8272 

8277 

8281  8286  8290 

8295 

8299  8304 

8308 

8313 

962  8318 

8322 

8327  8331;  8336 

8340i 

8345  8349 

8354 

8358 

963  8363 

8367 

8372  83761  8381 

8385 

8390  8394 

8399 

8403 

964  8408: 

8412 

8417  8421 

8426 

8430! 

8435  8439 

8444 

8448 

965  8453 

8457 

8462  8466 

8471 

8475 

8480  8484 

8489 

8493 

966  84S8 

8502 

8507  8511 

8516 

8520 

8525  8529 

8534 

8538 

967  8543: 

8547 

8552  8556 

8561 

85651 

8570  8574 

8579 

8583 

968  8586 

8592 

8597  86011  8605 

8610| 

8614  8619 

8623 

8628 

969  8632 

8637 

8641  8646'  8650 

86551 

8659  8664 

8668 

8673 

970  8677 

8682 

8686  8691  8695 

8700 

"87041J709 

8713 

8717 

971  8722 

8726 

8731  8735 

8740 

8744! 

8749  8753 

8758 

8762 

972  8767. 

8771 

8776  8780 

8784 

8789 

8793  8798 

8802 

8807 

973  8811 

8816 

8820  8825 

8829 

8834; 

8838  8843 

8847 

8851 

974  8856 

8860 

8665  8869 

8874 

8878 

8883  8887 

8892 

8896 

975  8900| 

8905 

8909  8914 

8918 

8923 

8927  8932 

8936 

8941 

976  8945! 

8949 

8954  8958 

8963 

8967 

8972  8976 

8981 

8885 

977  8989 

8994 

8998  9003 

9007 

9012 

9016  9021 

9025 

9029 

978  9034 

9038 

9043  047 

052 

056 

061  065! 

069 

074 

979  9078 

9083 

9087  092  096 

100  105  109,  114  118 

980  »123~| 

9127 

9131   136  I'M 

~145 

149  154 

158 

162 

981  9167 

9171 

9176   180   185 

189 

193   198 

202 

207 

982  921  1! 

9216 

9220  224  229 

233 

238  242 

247 

251 

983  9255; 

9260 

9264  269|  273 

277 

282  286 

291 

295 

984  9300' 

9304 

9308  313  317 

322 

326  330 

335 

339 

985  9344' 

9348; 

9352  357 

361 

366 

370  374 

379:  383 

986  93881 
987  9432 

9392i 
9436 

9396  401 
9441   445 

405i 
449 

4101  414  419 

454  458  463 

423-  427 
467  471 

988  9476' 

9480 

9484  499 

493 

498!  502  506 

511 

515 

989  9520; 

9524 

9528  533 

537 

542 

546  550 

555  559 

990  9564 

9568 

9572  577 

581 

~585 

590  ""594 

599~603 

991  9607  1 

9612 

9616  621 

625 

629 

634  638 

642J  647 

992  9651 

9656 

9660  664 

669 

673 

677  682 

686>  691 

9S3  9695 

9699 

9704^  708 

712 

717 

721  726 

73C 

734 

994  9739 

9743 

9747:  752 

756 

760 

765  760 

774 

778 

995  9782 

9787 

9791   795 

800 

804 

808  813 

817 

822 

936  9826 

9830 

9835  839 

843 

848 

852.  856 

861 

865 

997!  9870 

9874 

9878  883 

887 

891 

896;  900 

904 

909 

9981  9913 

9917 

9922  926 

930 

935 

939;  944 

94£ 

952 

9991  9957 

9961 

9965;  97C 

974 

978 

983:  987 

991 

996 

KO.j   0 

1 

'2  j"  3 

4 

5 

~T~[^7~ 

8 

9 

Artificial  Sines,  Tangents,  and  Secants* 


(fbegree. 

M 

Sine      C.  Sine 

Tang,  i 

C.Tang. 

Secant.  I 
lO.OOOOOl 
00' 
00 
00 
01 
01 
02 

C.  Sec.| 
Infinite 
12.83730 
53627 
36018 
23525 
13834 
05915 

J\l 

0 
5 

.1 
35 
40 
45 
50 
55 
60 

0.00000 
7.16270! 
463731 
63982 
76475 
86166! 
94084 
8.00779 
06578 
11693 
16268 
20407 
24186 

10.00000 
00 
00 
00 
9.99999 
99 
98 

0.00000 
7.16270 
46373 
63982 
76476 
86167 
94086 

Infinite 
12.83730 
53627 
36018 
23524 
13833 
05914 

60 
55 
50 
45 
40 
35 
30 
"23 
20 
15 
10 
5 
0 

9.99998 
97 
96 
95 
94 
93 

8.00781 
06581 
11696 
16273 
20413 
24192 
C.Tang. 

11.99219 
93419 
88304 

83727 
79587 
75808 
Tang. 

10.00002 
03 
04 
05 
06 
07 

11.99221 
93422 
88307 
83732 
79593 
75814 

M 

C.Sine 

Sine 

C.   Sec. 

Secant 

M 

89  Decrees. 

1  Degree. 

Secant.   C.  Sec. 

"M 

60 
55 
50 
45 

35 
30 

M 

Sine 
8.24186 
27661 
30879 
33875 
36678 
39310 
41792 

C.  Sinei  Tang. 

C.Tang. 

0 
5 
10 
15 

20 
25 
30 

9.99993 
92 
91 

89 

88 
87 
85 

8.24192 
27669 
30888 
33886 
36689 
'  39323 
41807 
8.44156 
46385 
48505 
5052' 
5245S 
5430* 
CTTa^ 

11.75808 
72331 
69112 
66114 
63311 
60677 
58193 

10.00007 
08 
09 
11 
12 
13 
15 

11.75814 
72339 
69121 
66125 
63322 
60690 
58208 

35 
40 
45 
50 
55 
60 

8.44139 
46366 
48485 
50505 
52434 
54282 

9.99983 

82 
80 
78 
76 
74 

11.55844 
53615 
1      51495 
49473 
47541 
M      45692 

10.00017 
18 

2C 

22 
24 
2C 

11.55861 
53634 
51515 

49495 
1      47566 

>      4571S 

1  25: 
20 

1( 

( 

M 

M 

C.  Sine 

Sine 

Tang. 

C.  Sec.  Secant. 

88  Degrees. 

M 

2  Degrees. 

"M 

Sine    1  C.  Sine]  Tang. 

C.Tang, 

|  Secant  jC.  Sec 

0 
5 

10 
15 

20 

25 
30 

8.54282 
56054 
57757 
59395 
60973 
62496 
63968 
1  8.65391 
!      66769 
68104 
»       6940C 
70655 
)       7188C 
[  C.  Shu 

9.99974 
71 
69 
6C 
64 
61 
5J 

8.6430811.45692 
56083       43917 
57788       42212 
59428       40572 
61009       38991 
62535;      37465 
1      64009       35991 

10.0002( 
21 

31 
3^ 

a 

3< 

41 

5111.45718    60 

)       43946   55 
42243    50 
\      40605   45 
!      39027   40 
>       S7504J  3.5 
|      36032J  30 

35 
4C 
4£ 
5C 
5£ 
6( 

9.9995t 
X 

? 

4< 
4( 

\    Sine 

}    8.6543511.34565 
}       66816.      33184 
)       68154;      31846 
69453  j      30547 
t       707141      29286 
)|      71940;      28060 

10.0004^ 
4' 
5( 
bi 
5* 
6C 

U1.3460S 

rl      33231 
)j      3189( 
.;      S060C 
.!      2934i 
>       2812C 
Secant 

>   25 
j  20 
5!  15 
>•  10 

i 

1     I 

M 

iC.Tangj  Tang.  |C.  Sec 

M 

87  Degrees. 

Artificial  Sines,  Tangents,  and  Secants. 


&  Degrees. 

M|  Sine 

|  C.  Sine 

Tang.  C.Tang.  Secant 

C.  Sec.i  M 

0 

5 
10 
15 

20 

25 
30 

8.7188C 
7306J 

74226 
7535S 
76451 

77522 
78567 

)  9.99940  8.7194011.28060 
37   73132   26868 
r    34   74292   25708 
U    30   754231   24577 
26j   76525!   23475 
2Sj   77600   22400 
19l   78649   21351 

10.0006011.281201  60 
63   26931  55 
66   25774  50 
70   24647  45 
74   23549  40 
77   22478  35 
81   21433  SO 

35 
40 
45 
50 
55 
60 

i  8.79588  9.99915 
80585     11 
81560'     07 
82513     03 
83446   99898 
84358    894 

8.79673  11.20327|  10.00085  11.20412 
80674   193261     89   19415 
81653   18347J     93J   18440 
82610;   17390     97   17487 
8354?'   16453    102   16554 
84464   15536    106   15642 

25 
20 
15 
10 
6 
0 

IS 

M  C.  Sine 

Sine 

C.Tang.  Tang.  1C.  Sec. 

Secant 

86  Degrees. 

4  Degrees. 

~M 

M 

Sine 
8.84358 
85252 
86128 
86987 
87829 
88654 
89464 

C.  Sine  j  lang. 
9.99894]  8.84464 
890   85363 
885   86243 
8801   87106 
876   87953 
871   88783 
866   8S598 

C.Tang. 
11.15536 
14637 

13757 
12894 
12047 
11217 
10402 

Secant 

C.  Sec. 

0 
5 
10 
15 

20 
25 
30 
~35 
40 
45 
50 
55 
60 

10.00106 
110 
115 
120 
124 
129 
134 

11.15642 
14748 
13872 
13013 
12171 
11346 
10536 

60 
55 
50 
45 
40 
35 
30 

8.90260 
91040 
91807 
92561 
93302 
94030 
C.  Sine 

9.99861 
856 
851 
845 
840 
834 

8.90399 
91185 
91957 
92716 
93462 
94195 

11.09601 
08815 
08043 
07284 
06538 
05805 

10.00139 
144 

166 

11.09740 
08960 
08193 
07439 
06698 
05970 

25 
20 
15 
10 
5 
0 

M 

Sine 

C.Tang.  Tang.  C.  Sec. 

Secant 

M 

85  Degrees. 

Degrees. 

M  Sine   C.  Sine; 

Tang.  |  C.Tang.  Secant 

C.  Sec. 

M 

"60 
55 
50 
45 
40 
35 
30 

0 
5 
10 
15 

20 
25 
30 

8.94030 
94746 
95450 
96143 
96825 
97496 
98157 
8.98808 
99450 
9.00082 
00704 
01318 
01923 
C.  Sine 

9.99834 
829 
823 
817 
812 
806 
800 

8.94195 
94917 
95627 
96325 
97013 
97691 
98358 

11.05805 
05083 
04373 
03675 
02987 
02309 
01642 
11.00985 
00338 
10.99699 
99070 
98450 
97838 

10.00166 
171 
177 

183 
188 
194 
200 

11.05970 
05254 
04550 
03857 
03175 
02504 
01843 
11.01192 
00550 
10.99918 
99296 
98682 
98077 

35| 

55 
60, 

9.99794 
787 
781 
775 
768 
761 

8.99015 
9.00301 

01550 
02162 

10.00206 
213 
219 

225 
232 
239 

25 
20 
15 
10 
5 
fe 

"M 

M! 

Sine 

C.Tang.  Tang.  C.  Sec. 

Secant 

84  Degrees. 

-Artificial  Sines.  Tangents,  and  Secants. 


6_Degrees. 

M, 

Sine   C.  Sine 

Tang.  C.Tang. 

Secant  (C.  Sec. 

M 

0 

if 
I 

25.; 

SO 

9.01924,  9.99761 
02520    755 
03109    748 
036901    741 
04263!    734 
04828    727 
05386    720 

9.02162  10.97838 
02765;   97235J 
03361   96639 
03949   96051 
04528   95472 
05101   94899 
05666   94334 

10.00239,1 

24* 
252 
259 
266 
2731 
280 
10.00287 
295 
302 
310 
317 
.  325 
C.  Sec. 

0.98076 
97480 
96891 
96310 
95737 
95172 
94614 

60 
55 
50 
45 
40 
35 
30 

I 

| 

9.05937  9.99713 
06481    705 
07018    698 
07548    690 
08072    683 
t)8589    675 

9.06224  10.93776 
06775   93225 
07320   92680 
07858   92142 
08389   91611 
08914   91086 

L0.94063! 
93519 
92982 
924521 
919281 
91411 

25 
20 
15 
10 

I 

1 

^1 

M 

C.  Sine  Sine  C.Tang.  Tang. 

Secant  | 

83  Degrees. 

7  Degrees. 

M| 

"o 

5 
10 
15 
20 

25 
30 

Sine 

C.  Sine!  Tang. 

C.Tang.j 

Secant  C.  Sec.) 

M 

"60 
55 
50 
45 
40 
35 
30 
"25 
20 
15 
1 

~M 

9.08589 
09101 
09606 
10106 
10599 
11087 
11570 
9.12047 
12519 
12985 
13447 
13904 
14356 

C.  Sine 

9.99675 
667 
659 
651 
643 
635 
627 

9.08914 
09434 
09947 
10454 
10956 
11452 
11943 

10.91086 
90566 
90053 
89546 
89044 
88548 
88057 

10.00325 
333 
341 
349 
357 
365 
373 

10.91411 
90899 
90394 
89894 
89401! 
88913 
88430J 

35 
40 
45 
50 
65 
60 

9.99618 
610 
602 
593 

584 
575 

9.12428 
12909 
13384 
13854 
14320 
14780 
C.Tang 

10.87572 
87091 
86616 
86146 
85680 
85220 

10.00382  10.87953 
390|   87481 
398|   87015 
407   86553 
416   86096 
.  425,,  85644 

M 

Sine 

Tang. 

C.  Sec.  Secant 

82  Degrees. 

8  Degrees. 

M 

Sine 

C.  Sine  j  Tang. 

C.Tang. 
10.85220 
84764 
84312 
83865 
83423 
82984 
82550 

Secant 

C.  Sec. 

M 

0 
5 
10 
15 

20 
''25 
30 
35 
40 
45 
50 
55 
60 

9.14356  9.99575  9.14780 
14803!    566   15236 
15245    557   15688 
15683    548   16135 
161161    539   16577 
165451    6301   17016 
16970    520   17450 

10.00425 
434 
443 
452 
461 
470 
480 
10.00489 
499 
508 
518 
528 
538 
C.  Sec. 

10.85644 
85197 
84755 
84317 
83884 
83455 
83030 

60 

f 

A 
4 

C. 

J 
~7 
<j 

15 
10 

9.17391 
17807 
1822C 
18628 
19033 
!   19433 

9.99511 
501 

492 

482 
47$ 
1    465 

I  9.17880 
18306 
18728 
1J9146 
.   19561 
\   19971 

10.82120 
81694 
81272 
80854 
80439 
80029 

10.82609 
82193 
81780 
81372 
80967 
80567 

M  C.  Sine  Sine 

C.Tang.  Tang. 

Secant 

M 

81  Degrees. 

24    Artificial  Sines,  Tangents,  and. Secants. 


9  Degrees. 

M 

~0 
5 
10 
15 

20 

25 
30 

Sine 

C.  Sine 

Tang. 
9.19971 

20378 
20782 
21182 
21578 
21971 
22361 

C.Tang. 
1080029 

79622 
79218 
78818 
78422 
78029 
77639 

Secant 
10.00538 
548 
558 
568 
579 
589 
600 

C.  Sec. 
10.80567 
80170 
79777 
79387 
79001 
78618 
78239 

M 

60 
55 
50 
45 
40 
35 
30 

"25 
20 
15 
10 
5 
0 
~M 

9.19433 
19830 
20223 
20613 
20999 
21382 
21761 

9.99462 
452 
442 
432 
421 
411 
400 
9.99390 
379 
368 
357 
346 
335 
Sine 

35 
40 
45 
50 
55 
60 

9.22137 
22509 
22878 
23244 
23607 
23967 
C.  Sine 

9.22747 
23130 
23510 
23887 
24261 
24632 
C.Tang. 

10.77253 
76870 
76490 
76113 
75739 
75368 

10.00610 
621 
632 
643 
654 
665 

10.77863 
77491 
77122 
76756 
76393 
76033 

M 

Tang. 

C.  Sec. 

Secant 

80  Degrees. 

10  Degrees. 

M 

~0 
5 
10 
15 

20 
25 
30 

Sine 

C.  Sine 

Tang.  C.Tang. 

Secant 

C.  Sec. 

M 

9.23967 
24324 
24677 
25028 
25376 
25721 
26063 
9.26403 
26739 
27073 
27405 
27734 
28060 

9.99335 
324 
313 
301 
290 
278 
267 

9.246321 
25000 
25365 
25727 
26086 
26443 
26797 

10.75368 
75000 
74635 
74273 
73914 
73557 
73203 
10.72852 
72504 
72158 
71814 
71473 
71135 

10.00665 
676 

687 
699 
710 

722 
733 

10.76033 
75676 
75323 

.  74972 
74624 
74279 
73937 

6C 
55 
50 
45 
40 
35 
30 

35 
40 
45 
50 
55 
60 

9.99255 
243 
231 
219 
207 
195 

9.27148 

27496 
27842 
28186 
28527 
28865 
C.Tang. 

10.00745 

757 
769 
781 
793 
806 

10.73597 
73261 

72927 
72595 
72266 
71940 

25 
20 
15 

10 
^ 

0 

M 

C.  Sine] 

Tang.  C.  Sec. 

Secant 

M 

79  Degrees. 

11  Degrees. 

M 

Sine   C.  Sine 

Tang. 

C.Tang. 

Secant 

C.  Sec. 

M 
~60 
55 
50 
45 
40 
35 
30 

0 
5 

10 
15 

20 
25 
30 
35 
40 
45 
50 
55 
60 

9.28060 
28384 
28705 
29024 
29340 
29654 
29966 
9.30275 
30582 
30887 
31189 
31490 
31788 
C.  Sine 

9.99195 
182 
170 
157 
145 
132 
119 

9.28865 
29201 
29535 
29866 
30195 
30522 
30846 

10.71135 
70799 
70465 
70134 
69805 
69478 
69154 

10.00805 
818 
830 

843 
855 
868 
881 

10.71940 
71616 
71295 
70976 
70660 
70346 
70034 

9.99106 
093 
080 
067 
054 
040 

9.31168 
31489 
31806 
32122 
32436 
32748 

10.68832 
68511 
68194 
67878 
67564 
67252 

10.00894 
907 
920 
933 
946 
960 
C.  Sec. 

10.69725 
69418 
69113 
68811 
68510 
68212 

25 
20 
16 
10 
5 

0 

M 

Sine 

C.Tang. 

Tang. 

Secant 

M 

78  Degrees. 

Artificial  Sines,  Tangents,  and  Secants. 


12  Degrees.                 ( 

M 

0 
5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
~M 

Sine 

C.  Sine  Tang.  C.Tang. 

Secant  iC.  Sec.! 

M 
60 
55 
50 
45 
40 
35 
30 
"25 
20 
15 
10 
5 
0 

9.31788 
32084 
32378 
32670 
32960 
33248 
33534 

9.99040  9.32747 
99087   33057 
99013   33365 
99000   33670 
98986   33974 
98972   34276 
98958   34576 

10.67253 
66943 
66635 
66330 
66026 
65724 
65424 
10.65126 
64830 
64536 
64243 
63958 
63664 
Tang. 

10.00960 
00973 
00987 
01000 
01014 
01028 
01042 

10.01056 
01070 
01084 
01099 
01113 
01128 

10.68212 
67916 
67622 
67330 
67040 
66752 
66466 
10.66182 
65900 
6-5620 
65342 
65066 
64791 

9.33818;  9.98944  9.34874 
34100   98930   35170 
34380   98916   35464 
34658   98901   35757 
34934   98887   36047 
85209   98872   36336 

C.  Sine 

Sine  C.Tang. 

C.  Se<c.  Secant 

M 

77  Degrees. 

13"  D'egrees. 

M 

Sine 
9.35209 
35482 
35752 
36022 
36289 
36555 
36818 

C.  Sine!  Tang.  J  C.Tang. 

Secant 

fOJOU28 
01142 
01157 
01172 
01187 
01202 
01217 

C.  Sec. 

M 

0 
5 
10 
15 

20 
25 
80 

9.988721  9.36336 
98858!   36624 
98843   36909 
98828   37193 
98813   37478 
98798   37756 
98783;   38035 

10.63664 
63376 
63091 
62807 
62524 

61965 

10.64791 
64518 
64248 
63978 
63711 
63445 
63182 

60 
55 
50 
45 
40 
35 
30 

35 
40 
45 
50 
55 
60 

M 

9.37081 
37341 
37600 
!   37858 
38113 
38368 

9.98768  9.38313 
98753!   38589 
98737   38863 
98722!   39136 
987061   39407 
98690   39677 

10.61687 
61411 
61137 
60864 
60593 
60323 

10.01232 
01247 
01263 
01278 
01294 
01310 

10.62919 
62659 
62400 
62142 
61887 
61632 
Secant 

2( 
15 
10 
5 
0 

M 

C.  Sine 

[  Sine  C.Tang. 

Tang. 

C.  Sec. 

76  Degrees.   j 

M 

0 
5 
10 
15 

20 

25 
30 

14  Degrees. 

Sine 

C.  Sinej  Tang. 

C.Tang. 

Secant  jC.  Sec.  M 

9.38368  9.98690  9,39677  10.60323  10.01310 
38620;   98675!   39945   60055   01325 
38871   98659!   40212   59788   01341 
39121   98643'   40478!   59522   01357 
39369   98627   40742J   59258   01373 
39615   D8610:   41004   58996   01390 
39860   98594'   41266   58734   01406 

10.61632 
61380 
61129 
60879 
60631 
60385 
60140 

60 
55 
SO 
45 
40 
35 
30 

35 
40 
45 
50 
55 
60 
"M 

9.40104 
40345 
40586 
40825 
41063 

;    41300 

C.  Sine 

9.98578  9.41526  10.58474  10.01422 
-98561   41784   58216'   01439 
98545   42042   57958!   01455 
98528   42297   57703j   01472 
98511!   42552   57448   01489 
98494   42805   57195;   01506 

10.59896 
59655 
59414 
59175 
58937 
58700 

25 
20 
15 
10 
5 
0 

Sine  iC.Tang.i  Tang. 

C.  Sec.  1  Secant 

M 

75  Degrees. 

26    Artificial  Sines,  Tangents,  and  Secants. 


15  Degrees. 

M 

5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
JM 

Sine 

C.Sine 

Tang.  C.Tang. 

Secant  \ 

C.  Sec.i  M 

9.41300  9.98494  9.4280510.57195 
41535   98477   43057   56943 
41768   98460   43308   56692 
42001   98443   43558   56442 
42232   98426   43806   56194 
42462   98409|   44053   55947 
42690   98391   44299   55701 

10.01506 
01523 
01540 
01557 
01574 
01591 
01609 
10.01626 
01644 
01662 
01680 
01698 
01716 

10.587001  60 
58465!  55 
58232  50 
67999  45 
57768  40 
57538  35 
57310  30 

9.42917 
43143 
43368 
43591 
43813 
44034 

9.98374 
98356 
98338 
98320 
98302 
98284 

9.44544  10.55456 
44787  55213 
45029  54971 
45271  54729 
45511  54489 
45750  54250 

10.57083 
56857 
66632 
56409 
56187 
55966 

25 
20 
15 
10 

C 

C.  Sine 

Sine 

C.Tang.  Tang. 

C.  Sec. 

Secant  I  M 

74  Degrees. 

* 

16  Degrees. 

M 
~0 

5 
10 
16 

20 
25 
30 

Sine 

C.  Sine 

Tang.  [C.Tang. 

Secant 

C.  Sec. 

M 

9.44034 
44253 
44472 
44689 
44905 
45J20 
45334 

9.98284 
98266 
98248 
98229 
98211 
98192 
98174 

9.4575010.54250 
45987J  54013 
462241  53776 
46460J  53540 
46694!  53306 
46928!  53072 
471601  52840 

10.01716 
01734 
01752 
01771 
01789 
01808 
01828 
10.01845 
01864 
01883 
01902 
01921 
01940 

10.55966 
55747 
55528 
55311 
55095 
54880 
54666 

60 
55 
50 
45 
40 
35 
SO 

35 
40 
45 
50 
55 
60 

"M 

9.45547  9.98155J  9.4739210.52608 
45758!   98136   47622   52378 
45969   98117i   47852J   52148 
461781   98098   48080   51920 
46386   98079   48307   51693 
46594   98060   48534.   51466 

10.54453 
54242 
54031 

53822 
53614 
53406 

Secant 

25 
20 
15 
10 
5 
0 

C.Sine 

Sine 

C.Tang.  Tang. 

C.  Sec. 

M 

73  Degrees. 

17  Degrees. 

1 

5 
10 
15 
20 
25 
30 

Sine 
9.46594 
46800 
47005 
47209 
47412 
47613 
47814 

C.Sine  Tang.  C.Tang. 

Secant 

C.  Sec,'  M 

9.98060  9.4853410.51466 
98040   48759   51241 
98021   48984   51016 
98001   492071   50793 
979821   49430!   50570 
97962   496521   50348 
97942   49872i   50128 

10.01940  10.53406 
01960,   63200 
01979   52995 
01999   52791 
02018   52588 
020381   52387 
02058;   52186 
10.0207810,61986 
02098;   51787 
02118'   51589 
02139J   51392 
02159   51197 
021791   51002 

60 

5( 
45 
40 
35 
30 

35 
40 
45 

50 
55 
60 

M 

9.48014 
48213 
48411 
48608 
48803 
48998 
C.Sine 

9.97922 
97902 
97882 
97861 
97841 
97821 

9.50092  10.49908 
60311  49689 
50529  49471 
50746  49254 
50962  49038 
51178  48822 

25 
20 
15 
10 
5 
6 

Sine 

C.Tang.  Tang. 

C.  Sec. 

Secant 

72  Degrees. 

Artificial  Sines,  Tangents,  and  Secants*    27 


18  Degrees.                 , 

M 

Sine   C.  Sine  Tang.  C.Tangj  Secant  C.  Sec.;  M 

0 
5 
10 
15 
20 
25 
30 

9.48998! 
49192! 
49385 
49577 
49768 
49958 
50148 

9.97821  9.51178  10.48822  10.02179  1 
97800   61392   48608   02200 
97779i   51606   48394   02221 
97759   51819   481811   02241 
97738   52031   479691   02262 
97717!   52242   47758   02283 
97696:   52452;   47548!   02304 

0.51002  60 
50808  65 
50615  50 
50423  45 
50232  40 
50042  35 
49852  30 

35 

40 
45 
50 
55 
60 

IK 

9.50336  9.97674;  9.5266110.473391 
50523   97653;   52870   47130 
507101   97632'   63078   46922j 
50896'   97610:   53285i   46715i 
51080   97589   53492   46508 
51264   97567   53697   46303! 

0.02326 
02347 
02368 
02390 
02411 
02433 
C.  Sec. 

10.49664 
49477 
49290 
49104 
48920 
48736 

25 
20 
15 
10 
5 
0 

M 

C.  Sine  Sine  C.Tang. 

Tang. 

Secant 

71  Degrees. 

19  Degrees. 

M 

Sine  |  C.  Sine;  Tang.  1  C.Tang. 

Secant 

C.  Sec. 

M 

01  9.51264! 
5   51447 
10   51629 
15   51811 
20   51991 
25   52171 
30   52350 

9.97567,  9.53697110.46303 
97545   53902   46098 
97523   54106   45894 
9750l|   54309   45691 
97479   54512   45488 
97457  j   54714   45286 
97435j   54915   45085, 

10.02433 
02455 
02477 
02499 
02521 
02543 
02565 

10.48736 
48553 
48371 
48189 
48009 
47829 
47650 

60 
55 
50 
45 
40 
35 
30 

35  9.52527 
40;   52705 
45   52881 
50   o«3(Jo6 
55   53231 
60j   53405 

9.97412  9.551151 
973901   55315 
97367   55514 
97344!   55712 
S7322;   55910 
97299   56107 

10.44885 
44685 
44486 
44288 
44090 
43893 

10.02588 
02610 
02633 
02656 
02678 
02701 

10.47473 
47295 
47119 
46944 
46769 
46595 

25 
20 
15 
1 

~M 

M  C.  Sine  Sine  C.Tang. 

Tang. 

C.  Sec. 

Secant 

70  Degrees. 

20  Degrees. 

MI  Sine 

C.  Sine  Tang. 

C.Tang. 

Secant  C.  Sec.j  M 

0  9.53405 
5   53578 
10i   53751 
15   53922 
20   54093 
25   54263 
30,   54433 

9.97299  9.56107 
97275,   56303 
97262   56498 
97229i   56693 
972061   56887 
971821   57081 
97159   57274 
9.97135|  9.57466 
971  11  j   57658 
97087|   57849 
97063]   58039 
97039!   58229 
97015;   58418 

10.43893 
43697 
43502 
43307 
43113 
42919 
42726 

10.02701 
02725 
02748 
02771 
02794 
02818 
02841 
1002861 
1   0288S 
02912 
0293" 
02961 
0298* 
C.  Sec 

10.46595 
|   46422 
46249 
46078 
45907 
45737 
45567 

60 

i 

i 

35  9.54601 
40   54769 
45   54936 
50   55102 
55!   5526S 
60   55431 

10.42534 

42342 
42151 
41961 
41771 

41582 

10.45399 
>   45231 
t   45064 
4489S 
44732 
>   44567 

M  C.  Sine1  Sine  C.Tang 

Tang. 

.  Secant 

'. 

69  Degrees. 

§8     Artificial  Sines,  Tangents,  and  Secant*. 


21  Degrees. 

M 

~0 
5 
10 
15 
20 
25 
30 

Sine 
9.55433 
55597 
55761 
55923 
56085 
56247 
56408 
9.56568 
56727 
56886 
57044 
57201 
57358 

C.  Sine 

Tang. 

C.Tang. 

Secant 

C.  Sec. 

M 

9.97015 
96991 
96966 
96942 
96917 
96893 
96868 
9.96843 
96818 
96793 
96767 
96742 
96717 
Sine 

9.58418 
58606 
58794 
58981 
59168 
59354 
59540 

10.41582 
41394 
41206 
41019 
40832 
40646 
40460 

10.02985 
03009 
03034 
03058 
03083 
03107 
03132 

10.44567 
44403 
44239 
44077 
43915 
43753 
43592 

60 
55 
50 
45 
40 
35 
30 
~25 
20 
15 

10 

f 

0 

35 
40 
45 
50 
55 
60 

9.59725 
59909 
60093 
60276 
60459 
60641 

10.40275 
40091 
39907 
39724 
39541 
39359 

10.03157 
03182 
03207 
03233 
03258 
03283 

10.43432 
43273 
43114 
42956 
42799 
42642 

M 

C.  Sine 

C.Tang 

Tang. 

C.  Sec. 

Secant 

M 

68  Degrees. 

22  Degrees. 

M 

Sine 

C.  Sine 
9.96717 
96691 
96665 
96640 
96614 
96588 
96562 

Tang. 

C.Tang. 

Secant 

C.  Sec. 

M 

0 
5 
10 
15 

20 
25 
30 
~35 
40 
45 
50 
55 
60 

9.57358 
57514 
57669 
57824 
57978 
58131 
58284 
9.58436 
58588 
58739 
58889 
59039 
59188 
~C.  Sine 

9.60641 
60823 
61004 
61184 
61364 
61544 
61722 

10.39359 
39177 
38996 
38816 
38636 
38456 
38278 

10.03283 
03309 
03335 
03360 
03386 
03412 
03438 

10.42642 
42486 
42331 
42176 
42022 
41869 
417L6 

60 
65 
50 
45 
40 
35 
30 
~25 
20 

1C 
b 
0 

9.96535 
96509 
96483 
96456 
96429 
96403 

9.61901 
62079 
62256 
62433 
62609 
62785 

10.38099 
37921 
37744 
37567 
37391 
37215 
Tang. 

10.03465 
03491 
03517 
03544 
03571 
03597 

10.41564 
41412 
41261 
41111 
40961 
40812 

M 

Sine 

C.Tang. 

C.  Sec. 

Secant 

M 

67  Degrees. 

23  Degrees. 

M 

Sine   C.  Sine 

Tang. 

C.Tang.  Secant 

C.  Sec. 

M 

0 
5 
10 
15 
20 
25 
30 

9.59188 
59336 
59484 
59632 
59778 
59924 
60070 

9.96403 
96376 
96349 
96322 
96294 
36267 
96240 

9.62785 
62961 
63135 
63310 
63484 
63657 
63830 

10.37215 
37039 
36865 
36690 
36516 
36343 
36170 

10.03597 
03624 
03651 
03678 
03706 
03733 
03760 
10.03788 
03815 
03843 
03871 
03899 
03927 

C.  Sec. 

10.40812 
40664 
40516 
40368 
40222 
40076 
39930 

60 
55 
50 
45 
40 
35 
30 

35 
40 
45 
50 
55 
60 
M 

9.60215 
60359 
60503 
60646 
60789 
60931 

9,96212 
96185 
96157 
96129 
96101 
96073 

9.64003 
64175 
64346 
64517 
64688 
64858 

10.35997 
35825 
35654 
35483 
35312 
35142 

10.39785 
39641 
39497 
39354 
39211 
39069 

25 
20 
15 
10 
5 
P 

C.  Sine 

Sine 

C.Tang.'  Tang. 

Secant  1  M 

66  Degrees. 

Artificial  Sines,  Tangents,  and  Secants.    29 


24  Degrees. 

M 

Sine  | 
'9^0931 
61073; 
61214; 
61354 
614941 
61634! 
61773 

C.  Sine 

Tang.  C.Tang. 
9.64358  10.35142  i 
65028   34972 
65197;   34803 
65366   34634 
65535   34465 
65703   34297; 
65870   34130 

Secant  ( 
0.039271 
039551 
03983! 
04012 
04040 
04069 
04098J 

;.  Sec. 

M 

0 
5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 

9.96073 
96045 
96017 
95988 
95960 
95931 
95902 

10.39069 
38927 

38786 
38646 
38506 
38366 
38227 

60 
55 
50 
45 
40 
35 
30 

9.61911! 
62049i 
62186 
62323 
62459 
62595 
C.  Sine! 

9.95873  9.66038  10.33962  10.04127 
958441   66204   33796   04156 
95815   66371!   33629   04185 
95786!   66537   33463   04214 
95757  j   66702   33298   04243 
95728   66867'   38133   04272 

10.38089 
37951 
37814 
37677 
37541 
37405 

25 
20 
15 
10 

( 

M 

Sine 

C.Tang-. 

Tang.  ' 

C.  Sec. 

Secant 

M 

.  65  Degrees. 

25  Degrees. 

Ml  Sine 

C.  Sine 

Tang.  C.Tang. 

Secant  ;C.  Secj 

M 

60 
55 
50 
45 
40 
35 
30 

~25 
20 
1 

~M 

0 

10 
15 

20 
25 
30 
1J5 
40 
45 
5C 
55 
6C 

9.62595 
62730 
62865 
62999 
63133 
63266 
63398 
i  9.63551 
63662 
63794 
j   63924 
64054 
!   64184 
•  C.  Sine 

9.95728  9.66867 
95698   67032J 
95668   671961 
95639   67360 
95609   67524 
95579   67687 
95549|   67850 

10.33133 
32968 
32804 
32640 
32476 
32313 
32150 
10.31988 
31826 
31664 
31503 
31342 
31182 
Tang. 

10.04272 
04302 
04332 
04381 
04391 
04421 
04451 

10.37405 
37270 
37135 
37001 
36867 
36734 
36602 

9.95519 
95488 
95458 
9542T 
95391 
95366 

9.68012 
;   68174 
1   68336 
68497 
68658 
68818 

10.04481  10.36469 
04512   36338 
04542   36206 
04573   36076 
04603   35946 
04634   35816 

M 

Sine 

C.Tang. 

C.  Sec.  Secant 

64  Decrees. 

26  Degrees. 

M  Sine 

C.  Sine  Tang. 

C.Tang. 

Secant  IC.  Sec. 

M 

0  9.64184 
5   64313 
10   64442 
15   64571 
20;   64698 
25   64826 
30   64953 

9.95366;  9.68818 
95335!   68978 
95304   69138 
95273   69298 
95242   69457 
9£*11   69615 
95179   69774 

10.31182 
31022 
30862 
30702 
30543 
30385 
30226 

10.04634 
04665 
04696 
04727 
04758 
04789 
04821 

10.35816 
35687 
35558 
35429 
35302 
35174 
36047 

60 

5 

45 
40 
35 

Q 

35  9.65079;  9.95148;  9.6993210.30068 
40   65205!   95116   70089   29911 
45   65331  1   950841   70247|   29753 
50   654561   95052   70404   29596 
55   65580!   95020   70560!   29410 
60   65705   94988   70717   29283 

10.04852 
04884 
04916 
04948 
0498C 
1   05012 

10.34921 
34795 
34669 
34544 
34420 
34295 

25 

2 

1 
~M 

Mi  C.  Sine 

Sine 

1C.  Tang.1  Tang. 

!c.  Sec. 

Secant 

63  Degrees. 

30   •Artificial  Sines,  Tangents,  and  Secante, 


27  Degrees. 

M 

Sine   C.  Sine 

Tang.  C.Tang.j  Secant 

C.  Sec. 

M 
60 
55 
50 
45 
40 
35 
SO 

0 
5 

10 
15 

20 

1 

9.65705 
65828 
65952 
66075 
66197 
S6319 
66441 
9.66562 
66682 
66803 
66922 
67042 
67161 

9.94988 
94956 
94923 
9489) 
94858 
94826 
94793 

9.70717  10.29283 
70873!   29127 
730281   28972 
71184!   28816 
71339   28661 
71493   28507 
71648J   28352 

10.05012 
05044 
05077 
05109 
05142 
05174 
05207 

10.34295 
34172 
34048 
33925 
33803 
33681 
33559 
10.33438 
33318 
33197 
33078 
32958 
32839 

1 

s 

55 
60 

9.94760 
94727 
94694 
94660 
94627 
94593 

9.71802  10.28198 
719551   28045 
721091   27891 

72262'   27738 
72415   27585 
72567   27433 

10.05240 
05273 

05373 
05407 

25 
20 
15 
10 
5 
0 

M 

C.  Sine  Sine  C.Tang.  Tang.  ;C.  Sec.  Secant 

M 

62  Degrees. 

28  Degrees. 

M 

^ 

1 

10 
16 

20 
25 
30 

Sine   C.  Sine  Tang.  !  C.Tang. 

Secant 
10.05407 
05440 
05474 
05508 
05542 
05576 
05610 

C.  Sec. 

9.67161 

€7280! 
67398 
67515 
67633 
67750 
67866 

9.94593 
94560 
94526 
94192 
94458 
94424 
94390 
9.94355 
94321 
94286 
94252 
94217 
94182 

9.72567  10.27433 

72720   27280 
72872   27128 
73023   26977 
73175   26825 
733261   26674 
73476   26524 

10.32839,  60 
32720,  55 
32602  50 
32485  45 
32367  40 
32250  35 
32134  30 

35 
40 
45 
50 
55 
60 
IK 

9.67982 
68098 
68213 
68328 
68443 
68557 
C.  Sine 

9.73627  10.26373 
73777,   26223 
739271   26073 
74077J   25923 
74226   25774 
74375;   25625 

10.05645'  10.320181  25 
05679|   31902  20 
057141   31787  15 
05748)   31672  10 
05783   31557  5 
058181   31443  0 

Sine 

C.Tang.'  Tang.  iC.  See.:  Secant  j  M 

61  Degrees. 

29  Degrees. 

M 

1  Sine  ;  C.  Sine  Tang.  C.Tang.;  Secant  ,C.  Sec. 

,  M 

0  9.68557 
5   68671 
10   68784 
15   68897 
201   69010 
25!   69122 
30|   69234 

9.94182  9.74375  10.25625 
94147   74524   25476 
94112   74673   25327 
94076   74S21   25179 
940411   74969   25031 
94005   75117   24883 
93970^   75264   24736 

10.05818 
05853 
05888 
05924 
05959 
05995 
06030 

10.31443 
31329 
31216 
31103 
30990 
30878 
30766 

1030861 
30544 
30433 
30323 
30213 
30103 

1  60 
55 

50 
45 

40 
35 
!  30 

35;  9.69345 
40.   69456 
45]   69567 
fiCN   69677 
55   69787 
60J   69897 
"M!  C.£ine 

9.93934  9.75411  10.24589 
93898   75558;   24442 
93862   75705'   24295 
938261   75852   24148 
93789   75998   24002 
93753   76144;   23856 

10.06066 
06102 
06138 
06174 
06211 
06247 

;  25 

i  20 
15 
10 
5 

LJ 

I'M 

Sine  IC.Tang.  Tang. 

C.  Sec. 

Secant 

60  Degrees. 

Artificial  Sines,  Tangents,  and  Secants.    3 1 


30  Degrees. 

M 

0 
5 

10 
15 

20 

25 
30 

Sine 
9.69897 
70006 
70115 
70224 
70332 
70439 
70547 

C.  Sine 

Tang. 

C.TangjiSecant. 

C.  Sec. 
10.30103 
29994 
29885 
29776 
29668 
29561 
29453 

M 
60 
65 

50 
45 
40 
35 
30 
T5 
20 
15 
10 
5 
0 

9.93753 
93717 
93680 
93643 
93606 
93569 
93532 

9.76144 
76290 
76435 
76580 
76725 
76870 
77015 

10.23856 
23710 
23565 
23420 
23275 
23130 
22985 

10.06247 
06283 
06320 
06357 
06394 
06431 
06468 

35 

40 

£ 

55 

1 

9.70654 
70761 
70867 
70973 
71079 
71184 
C.  Sine 

9.93495 
93457 
93420 
93382 
93344 
93307 

9.77159 
77303 
77447 
77591 
77734 
77877 

10.22841 
22697 
22553 
22409 
22266 
22123 

10.06505 
06543 
06580 
06618 
06656 
06693 

10.29346 
29239 
29133 

29027 
28921 
28816 

Sine 

C.Tang. 

Tang. 

C.  Sec. 

Secant 

M 

59  Degrees. 

M 

31  Degrees. 

Sine 

C.  Sine 

Tang.  C.Tang.  Secant.  C.  Sec. 

M 

0 
5 
10 
15 

20 
25 
30 

"35 

40 
45 

! 

M 

8.71184 
71289 
71393 
71498 
71602 
71705 
71809' 

9.93307 
93269 
93230 
93192 
93154 
93115 
93077 

9.77877  10.22123  10.06693  10.28816 
78020   21980   06731   28711 
78163;   21837;   06770   28607 
78S06;   21694   06808   28502 
78448!   21552   06846   28398 
785901   21410   068S5   28295 
787321   21268   06923   28191 

60 
55 
50 
45 
40 
35 
SO 

9.71911 
72014 
72116 
72218 
72320 
72421 

9.93038 
92999 
92960 
92921 

92881 
92842 

9.78873 
79015 
79156 
79297 
79438 
79579 
CTTang. 

10.21126 

20985 
20844 
20703 
20562 
20421 

10.06962 
07001 
07040 
07079 
07119 
07158 

10.28089 
27986 
27684 
27782 
27680 
27579 

25 
20 
15 
10 
5 
0 

"M 

C.  Sine 

Sine 

Tang. 

C.  Sec.i  Secant. 

58  Degrees. 

32  Degrees. 

M 

M 

Sine 

C.  Sine  Tang.  C.'Tang.  Secant  C.  Sec. 

0 

,S 

15 

20 

25 
30 

9.  72421  i  9.92842 
72522   92803 
726221   92763 
72723   92723 
72823   92683 
72922   92643 
73022]   92603 

9.79579 
79719 
79860 
80000 
80140 
80279 
80419 

10.20421  10.07158 
20281   07197 
20140   07237 
20000.   07277 
19860J   07317 
19721   07357 
195811   07397 

10.27579 
27478 
27378 
27277 
27177 
27078 
26S78 

60 
55 
50 
45 
40 
35 
30 

35 
40 
45 
50 
55 
60 
-M 

9.73121 
73219 
73318 
73416 
73513 
73611 
C.  Sine 

9.92563 
92522 
92482 
92441 
92400 
92359 

9.80558 
80697 
80836 
80975 
81113 
81252 

10.19442 
19303 
19164 
19025 

18887 
18748 

10.07437 
07478 
07518 
07559 
07600 
07641 

10.26879 
26781 
26682 
26584 
26487 
26389 
Secant 

25 
20 
15 
10 
5 
0 
~M 

Sine 

C.Tang. 

Tang.  C.  Sec. 

57  Degrees.              ^ 

2    Artificial  Sines,  Tangents,  and  Secants. 


33  Degrees. 

M 

0 
5 
10 
15 
20 
25 
30 
35 
40 
45 
60 
55 
60 

Sine 

C.  Sine 

Tang. 

C.Tang. 

Secant 

C.  Sec. 

M 
60 
55 
50 
45 
40 
35 
30 
-25 
20 
15 
10 
5 
0 

9.73611 

73708 
73805 
73901 
73997 
74093 
74189 
9.74284 
74379 
74474 
74568 
74662 
74756 

9.92359 
92318 
92277 
92235 
92194 
92152 
92111 
9.92069 
92027 
91985 
91942 
91900 
91857 
Sine 

9.81252 
81390 
81528 
81666 
81803 
81941 
82078 

10.18748 
18610 
18472 
18334 
18197 
18059 
17922 

10.07641 
07682 
07723 
07765 
07806 
07848 
07889 

10.26389 
26292 
26195 
26099 
26003 
25907 
25811 

9.82215 
82352 
82489 
82626 
82762 
82899 
C.Tang. 

10.17785 
17648 
17511 
17374 

17238 
17101 

10.07931 
07973 
08015 
08058 
08100 
08143 

10.25716 
25621 
25526 
25432 
25338 
25244 

M 

C.  Sine 

Tang. 

C.  Sec. 

Secant 

M 

56  Degrees. 

34  Degrees. 

M 

Sine 

C,  Sine 

Tang. 

~9.  82899 
83035 
83171 
83307 
83442 
83578 
83713 

C.Tang. 

Secant 

C.  Sec. 

M 

0 
5 
10 
15 

20 
25 
30 

1J5 

40 
45 
50 
55 
60 

9.74756 
74850 
74943 
75036 
75128 
75221 
75313 

9.91857 
91815 
91772 
91729 
91686 
91643 
91599 

10.17101 
16965 
16829 
16693 
16558 
16422 
16287 

10.08143 
08185 
08228 
08271 
08314 
08357 
08401 

10.25244 
25150 
25057 
24964 

24872 
24779 
24687 

60 
55 
50 
45 
40 
35 
30 
"25 
20 

1C 
5 
0 

9.75405 
75496 
75587 
75678 
75769 
75859 

9.91556 
91512 
91469 
91425 
91381 
91336 

9.83849 
83984 
84119 
84254 
84388 
84523 

10.16151  10.08444 
16016   08488 
15881   08531 
15746   08575 
"15612   08619 
15477   08664 

10.24595 
24504 
24413 
24322 
24231 
24141 

M 

C.  Sine 

Sine 

C.Tang. 

Tang.  C.  Sec. 

Secant 

M 

55  Degrees. 

35  Degrees. 

M 

Sine 

C.  Sine 

Tang. 

C.Tang.  Secant. 

C.  Sec. 

M 

0 
5 

10 
15 
20 
25 
30 

9.75859 
75949 
76039 
76129 
76218 
76307 
76395 

9.31336 
91292 
91248 
91203 
91158 
91114 
91069 

9.84523 
84657 
84791 
84925 
85059 
85193 
85327 

10.15477 
15343 
15209 
15075 
14941 
14807 
14673 
10.14540 
14406 
14273 
14140 
14007 
13874 
^fanF 

10.08664 
08708 
08752 
08797 
08842 
08886 
08931 

10.08977 
09022 
09067 
09113 
09158 
09204 
C.  Sec. 

10.24141 
24051 
23961 
23871 
23782 
23693 
23605 

60 
55 
50 
45 
40 
35 
30 

35 

40 
45 
00 
55 
60 

9.76484 
76572 
76660 
76747 
76835 
76922 
C.  Sine 

9.91023 
90978 
90933 
90887 
90842 
90796 

9.85460 
85594 
85727 
85860 
85993 
86126 

10.23516 
23428 
23340 
23253 
23165 
23078 

25 
20 
15 
10 

C 
M 

M 

Sine 

C.Tang. 

Secant 

54  Degrees. 

Arlifcial  Sines,  Tangents,  and  Secants.    33 


M 

Sine 

C.  Sinej 

Tang. 
"9T86126 
86259 
86392 
86524 
86656 
86789 
86921 

C.Tang.  Secant  i< 
10.1387410.09204 
13741   09250 
13608   09296 
13476   09343 
13344   09389 
1321  I1   09435 
13079   09482 

J.  Sec.i 

Ml 

\ 

B 

20 
i  25 
30 

9.76922 
77009 
77095 
77181 
77268 
77353 
77439 

9.90796 
90750 
90704 
90657 
90611 
90565 
90518 

10.23078 
22991 
22905! 
22819, 
22732 
22647 
22561 

601 
551 
50* 
451 

401 
351 

301 
25 
20 
15 

li 

0, 

35 

40 
45 
50 
55 
60 

9.77524  9.90471 
77609   90424 
77694   90377 
77778   90330 
77862   90282 
77946   90235 

9.87053 
87185 
87317 
8744? 
8758C 
8771J 

10.12947  10.09529 
12815   09576 
12683   09623 
12552   09670 
12420   09718 
1   12289   09765 

10.22476 
22391 

22306 
22222 
22138 
22054 

I  Mi  C.  Sine  Sine 

C.Tang 

.  Tang.  C.  Sec. 

Secant 

M. 

53  Degrees. 


37  Degrees. 


Ml  Sine 
0!  9.77946 
5   78030 
10   78113 
i  15   78197 
20-   78280 
25   78362 
30   78445 

C.  Sine,  Tang.  ;< 

S.TangJ 

10.12289; 
12157  1 
12026: 
11895! 
11764 
11633| 
11502 

Secant  j< 
LO.  097651 
09813; 
09861! 
09909! 
09957; 
10005 
10053, 

3.  Sec.i 

a 

601 
551 

50] 
451 

40 
351 

1 

5 

10 

j 

M 

9.90235 
90187 
90139 
90091 
90043 
89995 
89947 

9.87711 

87843 
87974 
88105: 
88236! 
88367! 
88498 

0.22054; 
21970; 
21887 
21803 
21720 
21638 
21655 
10.21473 
21391 
21309 
21228 
21147 
21066 

ra 

S 

55j 

1  H 
rai 

9.78527 
78609 
77691 

78772 
78853 
78934 

9.89898 
89849 
89801 
89752 
89702 
89653 

9.88629 
88759 
88890 
89020 
89151 
89281 

10.11371 
11241 
11110 

10980 
10849 
10719 

10.10102 
10151; 
10199| 
10248 
10298 
10347 

C.  Sine  Sine  C.Tang. 

Tang. 

1C.  Sec. 

Secant 

1                 52  Degrees.                 | 

38  Degrees. 


M 

Sine  j  C.  Sinej 

Tang.  |C 
9.89281  10 
89411 
895411 
8967  Ij 
89801  1 
89931! 
90061! 

Tang. 
.10719 
10589 
10459 
10329 
10199 
10069 
09939 

Secant 
10T0347 
10396 
10446 
10496 
10545 
10595 
10646 
10.10696 
10746 
10797 
10848 
10899 
10950 
1C.  Sec. 

C.  Sec. 
10.21066 
20985 
20905 
20824 
20744 
20685 
20585 

M 

0 
5 
10 
15 
20 
25 
30 

9.78934i 
79015 
79095 
791761 
79256; 
79335J 
79415 

9.89653| 
89604' 
89554; 
89504' 
89455! 
89405! 
89354! 

60 
55 
50 
45 
40 
35 
r30 
|  25 
i  20 

i  15 
10 
5 
1  -0 

35:  9.79494 
40!   79573 
45i   79652 
50   797311 
55!   "79809 
i  60   79887 

9.89304, 
89254 
89203 
89152 
8910l| 
89050J 

9.9019010.09810 
90320   09680 
90449J   09551 
90578   09422 
90708;   09292 
90837!   09163 
C.TangJ^a^T 

10.20506 
20427 
20348 
20269 
20191 
20113 

M  C.  Sine 

Sine  I 

Secant 

M 

51  Degrees. 
8 


34    Artificial  Sines,  Tangents,  and  Secants, 


39  Degrees.                , 

M 

~0 
5 
10 
15 

20 

25 
30 

Sine 
9.79887 
79965 
80043 
80120 
80197 
80274 
80351 
9.80428 
80504 
80580 
80656 
80731 
80807 

C.  Sine 

Tang. 

C.Tang. 
10.09163 
09034 
08905 
08776 
08647 
08518 
08390 

Secant 

C.  Sec. 

M 
"60 
55 
50 
45 
40 
35 
30 

9.89050 
88999 
88948 
88896 
88844 
88793 
88741 

9.90837 

GAncc 

yuyoo 
91095 
91224 
91353 
91482 
91610 
9.91739 
91868 
91996 
92125 
92253 
92381 
C.Tang. 

10.10950 
11001 
11052 
11104 
11156 
11207 
11259 

10.20113 
20035 
19957 
19880 
19803 
19726 
19649 

35 

40 
45 
50 
55 
60 

9.88688 
88636 
88584 
88531 
88478 
88425 
Sine 

10.08261 
08132 
08004 
07875 
07747 
07619 

10.11312 
11364 
11416 
11469 
11522 
11575 

10.19572 
19496 
19420 
19344 
19269 
19193 

25 
20 
15 
10 
5 
0 

M 

C.  Sine 

Tang. 

C.  Sec. 

Secant 

M 

50  Degrees. 

40  Degrees. 

M  Sine 

C.  Sine 

Tang. 

C.Tang. 

Secant 

C.  Sec.  M 

0 
5 
10 
15 
20 
25 
30 

9.80807 
80882 
80957 
81032 
81106 

enso 

81254 

9.88425 
88372 
88319 
88266 
88212 
88158 
88105 

9.92381 
92510 
92638 
92766 
92894 
93022 
93150 

10.07619 

07490 
07362 
07234 
07106 
06978 
06850 

10.11575 
11628 
11681 
11734 

11788 
11842 
118y5 

10.19193 
19118 
19043 
18968 

18S94 
18820 
18746 

6U 
55 
50 
4* 
40 
35 
30 

35 
40 
45 
50 
55 
60 

M 

9.81328 
81402 
81475 
81549 
81622 
81694 

9.88050 
8t996 
87942 
87887 
87833 
87778 

9.93278 
93406 
93533 
93661 
93789 
93916 

10.0672210.11950 
06594   12004 
06467   12058 
06339   42113 
06211   12167 
06084   12222 

10.18672 
18598 
18525 
18451 
18378 
18306 

25 

24} 
15 
10 

o 

C.  Sine 

Sine 

C.Tang. 

Tang.  C.  Sec. 

Secant 

M 

49  Degrees. 

41  Degrees. 

M 

Sine 
9.81694 
81767 
61839 
81911 
81983 
82055 
82126 

C.  Sine 

Tang. 

C.Tang. 

Secant 
10.12222 
12277 
12332 
12387 
12443 
12499 
12554 
10.12610 
12666 
12723 
12779 
12836 
12893 

C.  Sec. 
10.18366 
18233 
18161 
18089 
18017 
17945 
17874 
10.17802 
17731 
17660 
17590 
17619 
17449 

M 

60. 
65 
50 
45 
40 
35 
30 
"25 
29 
15 
1Q 
5 
0 
-M 

0 
5 
10 
15 

20 
25 
SO 

9.87778 
87723 
87668 
87613 
87557 
87501 
87446 

9.93916 
94044 
94171 
94299 
94426 
94554 
94681 

10.06084 
05956 
05829 
05701 
05574 
05446 
05319 

35 
40 
45 
5G 
5fi 
6C 

9.82198 
82269 
82340 
82410 
82481 
82551 

9.87390 
87334 
87277 
87221 
87164 
87107 

9.94808 
94935 
95062 
95190 
95317 
95444 

10.05192 
05065 
04938 
04810 
04683 
04556 

M 

C.  Sine 

Sine 

C.Tang. 

Tang. 

C.  Sec. 

Secant 

48  Degrees. 

Artificial  Sines,  Tangents,  and  Secants.    35 


42  Degrees.                | 

M 

Sine  | 

C.  Sine 
9.87107 
87050 
86993 
86936 
86879 
86821 
86783 

Tang,  j 
9.95444 
95571 
95698 
95825 
95952 
96078 
96205 

C.Tang. 

Secant. 

C.  Sec. 
10.17449 
17379 
17309 
17239 
17170 
17101 
17032 

M 

0 

I 

15! 

n 

30 

35 
40 
45 
50 
55 
60 

9.82551; 

82621 
82691 
827611 
82830, 
82899 
82968 

10.04556 
04429 
04302 
04175 
04048 
03922 
03795 

10.12893 
12950 
13007 
13063 
13121 
13179 
13237 

60 
&5 
50 
45 
40 
35 
30 
-25 
20 
15 
10 
5 
0 

9.83037 
83106 
83174i 
83242; 
83310| 
83378; 
C.  Sine! 

9.86705 
86647 
86589 
86530 
86472 
86413 

9.96332 
96459 
96586 
96712 
9G839 
96966 

10.03668 
03541 
03414 
03288 
03161 
03034 

10.13295 
13353 
13411 
13470 
13528 
13587 

10.16963 
16894 
16826 
16758 
16690 
16622 
Secant 

M: 

Sine  iC.Tang. 

Tang. 

C.  Sec. 

M 

47  Degrees. 

M 

43  De 

Tang. 
9.96966 
97092 
97219 
97345 
97472 
97598 
97725 

grees. 

C.  Sine 

C.  Tang..  Secant.  ;C.  Sec. 

i  M 

0  9.83378 
5   83446 
10   83513 

15|   83581 
20|   83648 
25   83715 
30!   83781 

9.86413 
86354 
86295 
86235 
86176 
86116 
86056 

10.03034 
02908 
02781 
02655 
02528 
i   02402 
02275 

10.13587 
13646 
13705 
13765 
13824 
13884 
13944 

10.16622 
16554 
16487 
16419 
16352 
16285 
16219 

60 
55 
!  50 
45 
!  40 
35 
30 

35 
40 
45 
50 
55 
60 

9.83848 
83914 
83980 
84046 
84112 
84177 
lc7Sin~e 

9.85996  9.97851 
85936:   97978 
85876   98104 
85815   98231 
85754'   98357 
85693!   98484 
Sine  CTTang, 

10.02149 
02022 
01896 
01769 
01643 
01516 

10.14094 
14064 
14124 
14185 
14246 
14307 

10.16152 
16086 
16020 
15954 

1588S 
15823 

i  25 
1  20 
!  15 
10 
5 
0 

M 

Tang.  C.  Sec. 

Secant. 

M 

46  Decrees. 

44  Degrees. 

M 

Sine 
9.84177 
84242 
84308 
81373 
64437 
84502 
84566 
9.84630 
84694 
84758 
84822 
>   84885 
>1   84949 

C.  Sine  Tang. 

C.Tang 

Secant  C.  Sec. 

M 

0 
5 
10 
15 

20 

25 
30 

9.85693;  9.98484  10.01516 
85632:   98610   01390 
85571!   98737   01263 
85510;   98863   01137 
85448J   98989   01011 
85386]   99116!   00884 
85324|   992421   00758 

10.1430710.15823 
14368   15758 
14429   15692 
14490   15627 
14552   15563 
14614   15498 
14676   15434 

60 

:  55 

50 
45 
40 
35 

30 

35 
4C 
4L 
5C 
5£ 
6{ 

9.85262 
8520( 
8513' 
8507^ 
85015 
84945 

.  9.99368 
)   99495 
r   99621 
I   99747 
\   99874 

no.ooooc 

10.00632 
0050S 
0037S 
00253 
00126 
10.0000C 

10.14738 
14800 
14863 
14926 
14988 
15051 

10.15370  25 
15306!  20 
15242  \  15 
15178  10 
15115J  5 
15051  0 

M  C.  Sine 

Sine 

IC.Tang.!  Tang. 

Secant 

"M 

45  Degrees. 

36  TRAVERSE  TABLE. 


III.  A  TRAVERSE  TABLE,  or  TABLE  OF  DIFFERENCE  OF  LATI- 
TUDE AND  DEPARTURE ,  calculated  for  degrees  and  quarters  of 
degrees,  and  for  any  distance  up  to  100  Rods,  Chains,  &c. ;  by 
which  the  northings  and  southings,  eastings  and  westings  made 
in  a  Survey  may  be  found. 

JVofe.  Northings  and  southings  are  called  Difference  of  Latitude,  pr  simply 
Latitude ;  eastings  and  westings  are  called  Departure,  Meridian  Dis- 
tance, or  Longitude. 

Explanation  of  the  Table. 

To  find  the  Latitude  and  Departure,  or  Northing ,  $c.  for  any 
Course  and  Distance. 

Jf  the  Course  be  less  than  45o,  look  for  it  at  the  top,  but  if 
more  than  45°  at  the  bottom  of  the  page,  and  look  for  the  Dis- 
tance in  the  right  or  left  hand  column ;  against  the  Distance, 
and  directly  under  or  over  the  Course,  stand  the  northing,  &c. 
in  whole  numbers  and  decimals. 

If  the  Course  be  less  than  45°,  the  northing  or  southing  will 
be  greater  than  the  easting  or  westing;  but  if  more  than  45°0 
the  easting  or  westing  will  be  the  greatest. 

When  the  Distance  exceeds  100,  take  any  two  or  more  num- 
bers, which,  added  together,  will  equal  the  Distance,  and  find 
the  Latitude  and  Departure  for  each  of  those  numbers ;  add 
the  several  Latitudes  together  and  the  sum  will  be  the  whole 
Latitude ;  and  so  for  the  Departure.  And  when  the  Distance 
is  in  Chains  and  Tanks,  or  whole  numbers  and  decimals,  find 
the  Latitude,  &c.  for  the  Chains  or  whole  numbers,  and  then 
for  the  Links  or  decimals,  remembering  to  remove  the  decimal 
point  in  the  Table  further  to  the  left,  according  to  the  given 
decimal. 

EXAMPLES. 

1.  Required  the  Latitude  and  Departure  for  45  Rpds,  on  a 
Course  JV.  15°  15'  W. 

Under  15°  15'  and  against  45  is  43.42  for  the  northing,  and 
11.84  for  the  westing. 

2.  Required  the  Latitude  and  Departure  for  120  Rods)  on  a 
Course  S.  58°  30/  E. . 


TBAVERSE  TABLE.  37 

Sake  one  third  of  120  which  is  40 ;  against  this  number, 
over  58°  30'  is  29.90  for  the  Latitude  and  34.11  for  the  De- 
parture. These  multiplied  by  3  give  62.70  for  the  Southing 
and  102.33  for  the  Easting;. 

3.  Required  the  Latitude  and  Departure  for  37.36  Rods  or  37 
Chains  and  36  Links,  on  a  Course  JV*.  26°  45'  E. 

For  37.  Lat.  33.04  Dep.  16.65 

0.36  .32  .16 

37.36  33.36  16.81 

Northing  33.36  Easting  16.81 

.Vote.  When  the  Minutes  are  not  15,  30,  or  45,  the  Northings,  &c.  must 
be  calculated  by  Natural  Sines,  or  by  Trigonometry. 


38 


TRAVERSE  TABLE, 


g 

iDegs 

iBefr 

f  Deg. 

g 

n 

Lat.  jDep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

j 

1.00;  0.00 

1.00 

0.01 

1.00 

0.01 

i 

2 

2.00  0.01 

2.00 

0.02 

2.00 

0.03 

2 

3 

3.00  0.01 

3.00 

0.03 

3.00 

0.04 

3 

4 

4.00  0.02 

4.00 

0.03 

4.00 

0.05 

4 

5 

5.00  0.02 

5.00 

0.04 

5.00 

0.07 

• 

6 

6.00   0.03 

6.00 

0.05 

6.00 

0.08 

e 

7 

7.00;  0.03 

7.09 

0.06 

7.00 

0.09 

"3 

8 

8.001  0.03 

,8.00 

0.07 

8.00 

0.10 

'8 

0 

9.00J  0.04 

9.00 

0.08 

9.00 

0.12 

9 

10 

10.00    0.04 

10.00 

0.09 

10.00 

0.13 

10 

II 

11.00  0.05 

11.00 

0.10 

11.00 

0.14 

11 

12 

12.00!  0.05  12.00 

0.10 

12.00 

0.16 

12 

13 

13.00:  o.oe'j  13.00 

0.11 

13.00 

0.17 

IS 

14 

14.00;  0.06!  14.00 

0.12 

14.00 

0.18 

14 

15  15.00   0.07J  15.00 

0.13 

15.00 

0.20 

15 

id  16.00   0.07  16.00 

0.14 

16.00 

0.21 

16 

1717.00   0.07 

17.00 

0.15 

17.00 

0.22 

17 

18 

18.00   0.08 

;i8.oo 

0.16 

18.00 

0.24 

18 

19  19.00   0.08 

19.09 

0.17 

19.00 

0.25 

19 

2020.00!  0.09 

[20.00 

0.17 

20.00 

0.26 

20 

21 

21.00   0.09 

21.00 

0.18 

21.00 

0.27 

21 

2222.00   0.10|  22.00 

0.19 

22.00 

0:29 

22 

2323.00   O.lOj  23.00 

0.20 

23.00 

0.30 

23 

2424.00  0.10  24.00 

0.21 

24.00 

0.31 

24 

2525.00   0.11  25.00 

0.22 

25.00 

0.33 

25 

2626.00   0.11:26.00 

0.23 

26.00 

0.34 

26 

2727.00   0.12  27.00 

0.24 

27.00 

0.35 

27 

2828.00   0.12128.00 

0.24 

28.00 

0.37 

28 

29i29.00   0.13129.00 

0.25 

29.00 

0.38 

2J 

30i30.00;  0.13  30.00 

0.26 

30.00 

0.39 

30 

3131.00   0.14  31.00 

0.27 

31.00 

0.41 

31 

3232.00  0.14;  32.00 

0.28 

32.00 

0.42 

32 

3333.00  0.14S  33.00 
3434.00   0.15!  34.00 

0.29  133.00 
0.30IJ34.00 

0.43 
0.45 

33 

34 

3535.00   0.1535.00 

0.31  135.00 

0.46 

35 

3636.00   0.1636.00 

0.31 

36.00 

0.47 

36 

3737.00   0.16  37.00 

0.32 

37.00 

0.48 

37 

3838.00   0.17  38.00 

0.33 

38.00 

0.50 

38 

3939.00   0.17J  39.00 

0.34 

39.00 

0.51 

39 

40:40.00   0.17  40.00 

0.35 

40.00 

0.52 

40 

4141.00   0.18  41.00 

0.36 

41.00 

0.54 

41 

4242.00   0.18  42.00 

0.37 

142.00 

0.55 

42 

4343.00   0.19 

43.00 

0.38 

143.00 

0.56 

43 

4444.00   0.  191  44.00 

0.38JI44.00 

0.58 

44 

4545.00   0.20  45.00 
4646.00   0.20146.00 

0.39145.00 
0.40|'46.00 

0.59 
0.60 

45 
46 

47  47.00  0.21 

47.00 

0.41 

;47.00j  0.62    47 

48 

48.00   0.21 

48.00 

0.42 

J48.00I  0.63   48 

4£ 

49.00*  0.21 

49.00 

0.43 

49.00   0.64   49 

5( 

150.00  0.22 

;so.oo 

0.44 

50.00 

0.65,  50 

§ 

Dep.  ;  Lat 

Dep.   Lat. 

Dep. 

7Z7 

Q 

89f  D  eg. 

89-»-Deg. 

89|  Deg.  P 

TRAVERSE  TABLE. 


39 


5 

iDeg. 

iDeg. 

£Deg. 

0 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

51 

51.00 

0.22 

51.00 

0.45 

1.00 

0.67 

51 

52 

52.00 

0.23 

52.00 

0.45 

2.00 

0.68 

52 

53 

53.00 

0.23 

53.00 

0.46 

3.00 

0.69 

53 

54 

54.00 

0.24 

54.00 

0.47 

4.00 

0.71 

54 

55 

55.00 

0.24 

55.00 

0.48 

5.00 

0.72 

55 

56 

66.00 

0.24 

56.00 

0.49 

6.00 

0.73 

56 

57 

57.00 

0.25 

57.00 

0.50 

7.00 

0.75 

57 

58 

58.00 

0.25 

58.00 

0.51 

7.99!  0.76 

58 

59 

59.00 

0.26 

59.00 

0.51 

58.99J  0.77 

59 

60 

60.00 

0.26 

€0.00 

0.52 

59.991  0.79 

60 

61 

61.00 

0.27 

61.00 

0.53 

60.99   0.80 

61 

62 

62.00 

0.27 

62.00 

0.54 

61.99   0.81 

62 

63 

63.00 

0.27 

63.00 

0.55 

62.99   0.82 

63 

64 

64.00 

0.28 

64.00 

0.56 

63.99!  0.84 

64 

65 

65.00 

0.28 

65.00 

0.57 

64.99   0.85 

65 

66 

66.00 

0.29 

66.00 

0.58 

65.99  ,  0.86 

66 

67 

67.00 

0.29 

67.00   0.58 

66.99    0.88 

67 

tib 

by.oti 

0.30 

68.00    0.59 

67.99   0.89 

68 

69 

69.00 

0.30 

69.00   0.60 

68.99    0.90 

69 

70 

70.00 

0.31 

70.00J  0.61 

69.99J  0.92 

70 

71 

71.00 

0.31 

71.00 

0.62 

70.99 

0.93 

71 

72 

72.00 

0.31 

72.00)  0.63 

71.99 

0.94 

72 

73 

73.00 

0.32 

73.00 

0.64 

72.99 

0.96 

73 

74 

74.00 

0.32 

74.00 

0.65 

73.99 

0.97 

7.4 

75 

75.00 

0.33 

75.00 

0.65 

74.99 

0.98 

75 

76 

76.00 

0.33 

76.00 

0.66 

75.99 

0.99 

76 

77 

77.00 

0.34 

77.00 

0.67 

76.99 

1.01 

77 

78 

78.0C 

0.34 

78.00 

0.68 

77.99 

1.02 

78 

79 

79.01 

0.34 

79.00 

0.69 

78.99 

1.03 

80 

80.0C 

0.35 

80.00 

0.70 

79.99 

1,05 

80 

81 

81.00 

0.35 

81.00 

0.71 

80.99 

1.06 

81 

82 

82.00 

0.36 

82.00 

0.72 

81.99 

1,07 

82 

83 

83.00 

0.36 

83.00 

•0.72 

82.99 

1.09 

83 

84 

84.GC 

0.37 

84.00 

0.73 

83.99 

1.10 

84 

86 

85.W 

0.37 

85.00 

0.74 

84.99 

1.11 

85 

86 

86.01 

0.38 

86.00 

0.76 

85.99 

1.13 

86 

87 

87.0C 

0.38 

87.00 

0.7 

86.99 

1.14 

87 

88    88.01 

0.38 

88.00 

0.7 

87.99 

1.15 

88 

89!  89.CC 

0.39 

89.00 

0.7 

88.99 

1.16    89 

90    90.0L 

0.39 

90.00 

0.7 

89.99 

1.18J  90 

91!  91.CKj 

0.40 

91.  OC 

0.7 

90.99 

1.19!  91 

92^  92.0C 

0.40 

92.09 

0.8 

91.99 

1.20    92 

93    93.0 

•  0.4 

93.00 

0.8 

92.99 

1.22   93 

94    94.0t 

0.4 

94.00 

0.8 

93.99 

1.23   94 

96    95.a 

0.4 

95.00 

0.8 

94.99 

1.24J  95 

96    96.CX 

0.42 

96.0C 

0.8 

95.99 

1.26!  9fl 

97    97.01 

0.42 

97.0C 

0.8 

96.99 

1.27;  97 

98    98.(K 

0.43 

98.0C 

0.8 

97.99 

1.28;  98 

99    99.0 

0.43 

99.0C 

0.8 

98.99 

1.30!  99 

1(X 

noo.oc 

0.44 

100.0C 

0.8 

99.98 

1.31  100 

s 

Dep 
J89il 

Lat 

Dep. 

Lat 

Dep. 

Ta7 

|5 

[89±Deg. 

891  Deg. 

40 


TRAVERSE  TABLE. 


g 

iDeg. 

"if  Dei. 

1  1  De*,. 

IfDeg. 

d 

en 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

)ep. 

r' 

1 

1.00 

0.02 

1.00 

0.02 

1.00 

0.03 

1.00 

0.03 

~~J 

2 

2.00 

0.03 

2.00 

0.04 

2.00 

0.05 

2.00 

0.06 

2 

3 

3.00 

0.05 

3.00 

0.07 

3.00 

0.08 

3.00 

0.09 

3 

4 

4.00 

0.07 

4.00 

0.09 

4.00 

0.10 

4.00 

0.12 

4 

5 

5.00 

0.09 

5.00 

0.11 

5.00 

0.13 

5.00 

0.15 

5 

6 

6.00 

0.10 

6.00 

0.13 

6.00 

0.16 

6.00 

0.18 

6 

7 

7.00 

0.12 

7.00 

0.15 

7.00 

0.18 

7.00 

0.21 

1 

8 

8.00 

0.14 

8.00 

0.17 

8.00 

0.21 

8.00 

0.25 

8 

9 

9.00 

0.16 

9.00 

0.20 

9.00 

0.24 

9.00 

0.28 

9 

10 

10.00 

0.17 

10.00 

0.22 

10.00 

0.26 

10.00 

0.31 

10 

11 

11.00 

0.19 

11.00 

0.24 

11.00 

0.28 

10.99 

0.34 

11 

12 

12.00 

0.21 

12.00 

0.26 

12.00 

0.31 

11.99 

0.37 

12 

13 

13.00 

0.23 

13.00 

0.28 

13.00 

0.34 

12.99 

0.40 

13 

14 

14.00 

0.24 

14.00 

0.31 

14.00 

0.37 

13.99 

0.43 

14 

15 

15.00 

0.26 

15.00 

0.33 

14.99 

0.39 

14.99 

0.46 

15 

16 

16.00 

0.28 

16.00 

0.35 

15.99 

0.42 

15.99 

0.49 

16 

17 

17.00 

0.30 

17.00 

O.rtt 

16.99 

0.45 

lfi.99 

0.52 

17 

18 

18.00 

0.31 

18.00 

0.39 

17.99 

0.47 

17.99 

0.55 

18 

19 

19.00 

0.33 

19.00 

0.41 

18.99 

0.50 

18.99 

0.58 

19 

20 

20.00 

0.35 

20.00 

0.44 

19.99 

0.52 

19.99 

0.61 

2-0 

21 

21.00 

0.37 

21.00 

0.46 

20.99 

0.55 

20.99 

0.64 

21 

22 

22.00 

0.38 

21.99 

0.48 

21.99 

0.58 

21.99 

0.67 

22 

23 

23.00 

0.40 

22.99 

0.50 

2-2.99 

0.60 

2299 

0.70 

2i 

24 

24.00 

0.42 

23.99 

0.52 

23.99 

0.63 

23.99 

0.73 

& 

25 

25.00 

0.44 

24.99 

0.55 

24.99 

0.65 

24.99 

0.76 

25 

26 

26.00 

0.45 

25.99 

0.57 

25.99 

0.68 

25.99 

0.79 

26 

27 

27.00 

0.47 

26.99 

0.59 

26.99 

0.71 

26.99 

0.83 

27 

28 

28.00 

0.49 

27.99 

0.61 

27.99 

0.73 

27.99 

0.86 

28 

29 

29.00 

0.51 

28.99 

0.63 

28.99 

0.76 

28.99 

0.89 

29 

30 

30.00 

0.52 

29.99 

0.65 

i',;}.99 

0.79 

29.99 

0.92 

30 

31 

31.00 

0.54 

30.99 

0.68 

30.99 

0.81 

30.99 

0.95 

31 

32 

32.00 

0.56 

31.99 

0.70 

31.99 

0.84 

31.99 

0.98 

32 

33 

32.99 

0.58 

32.99 

0.72 

32.99 

0.86 

32.98 

.01 

33 

34 

33.99 

0.59 

33.99 

0.74 

33.99 

0.89 

33.98 

.04 

34 

35 

34.99 

0.61 

34.99 

0.76 

34.99 

0.92 

34.98 

.07 

35 

36 

35.99 

0.63 

35  99 

0.79 

35.99 

0.94 

35.98 

.10 

36 

37 

36.99 

0.65 

36.99 

0.81 

36.99 

.0.97 

36.98 

.13 

37 

38137.99 

0.66 

37.99 

0.83 

37.99 

0.99 

37.98 

.16 

38 

3938.99 

0.68 

38.99 

0.85 

MM 

.02 

38.98 

.19 

39 

4039.99 

0.70 

39.99 

0.87 

39.99 

.05 

39.98 

.22 

40 

4140.99 

0.72 

40.99 

0.89 

40.99 

.07 

40.98 

.25 

41 

42  41.99 

0.73 

41.99 

0.92 

41.99 

.10 

41.98 

.28 

42 

43  42.99 

0.75 

42.99 

0.94 

42.99 

.13 

42.98 

.31 

43 

4443.99 

0.77 

43.99 

0.96 

13.99 

.15 

43.98 

.34 

44 

4544.99 

0.79 

44.99 

0.9^ 

44.99 

.18 

44.98 

.37 

45 

4645.99 

0.80 

45.99 

.oc 

45.99 

.20 

45.98 

.40 

46 

•  47  46.99 

0.82 

46.99 

.03 

46.^9 

.23 

46.98 

.44 

47 

48  47.99 

0.84 

47.99 

05 

47.98 

1.26 

47.98 

.47 

48 

49  48.99 

0.86 

48.99 

.07 

48.98 

1.28 

48.98 

.50 

49 

5049.99 

0.87 

49.99 

.09 

49.98 

1.31 

49.98 

.53 

50 

+1  Dep. 
^        F 

Lat. 

D^pT 

Lat. 

Oep. 

Lat. 

Dep. 

Lat. 

ts 

Q|89Deg. 

btffDeg. 

aSiDeg. 

881  L)eg. 

Q 

TRAVERSE  TABLE. 


41 


c 

iDeg. 

l{-Deg. 

H  Deg. 

IfDeg. 

2 

CO* 

-»• 

Lat. 

)ep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.jDep. 

»* 

51 

50.99 

0.89 

0.99 

.11 

0.98 

1.34 

0.98 

1.56 

51 

52 

31.98 

0.91 

1.99 

.13 

1.98 

1.36 

1.98 

1.59 

52 

53 

52.98 

0.92 

2.99 

.16 

2.98 

1.39 

2.98 

1.62 

53 

54 

53.99 

0.94 

3.99 

.18 

3.98 

1.41 

3.97 

1.65 

54 

55 

54.99 

0.96 

4.99 

.20 

4.98 

1.44 

4.97 

1.68 

55 

56 

55.99 

0.98 

5.99 

.22 

5.98 

1.47 

5.97 

1.71 

56 

57 

o6.99 

0.99 

6.99 

.24 

6.98 

1.49 

6.97 

1.74 

57 

58 

57.99 

1.01 

7.99 

1.27 

7.98 

1.52 

7.97 

1.77 

58 

59 

58.99 

1.03 

8.99 

1.29 

8.98 

1.54 

58.97 

1.80 

59 

60 

59.98 

1.05 

9.99 

1.31 

9.98 

1.57 

59.97 

1.83 

60 

61 

60.99 

1.06 

0.99 

1.33 

0.98 

1.60 

60.97 

1.86 

61 

62 

61.  9S 

1.08 

1.99 

1.35 

1.98 

1.62 

61.97 

1.89 

62 

63 

62.89 

1.10 

62.99 

1.37 

2.98 

1.65 

62.97 

1.92 

63 

64 

63.99 

1.12 

3.98 

1.40 

3.98 

1.68 

63.97 

1.95 

64 

65 

64.  9£ 

1.13 

4.98 

1.42 

64.98 

1.70 

64.97 

1.99 

65 

66 

65.99 

1.15 

65.98 

1.44 

65.98 

1.73 

65.97 

2.02 

66 

67 

66.99 

1.17 

6.98 

1.46 

66.98 

1.75 

66.97 

2.05 

67 

68 

67.99 

1.19J 

7.98 

1.48 

67.98 

1.78 

67.97 

2.08 

68 

69 

68.99 

1.20 

8.98 

1.51 

68.98 

1.81 

68.97 

2.11 

69 

70 

69.9S 

1.22 

69,98 

1.53 

69.98 

1.83 

69.97 

2.14 

70 

7L 

70.99 

1.24 

70.98 

1.55 

70.98 

1.86 

70.97 

2.17 

71 

72 

71.99 

1.26 

11.98 

1.57 

71.98 

1.88 

71.97 

2.20 

72 

73 

72.99 

1.27 

72.98 

1.59 

72.97 

1.91 

72.97 

2.23 

73 

74 

73.99 

1.29 

73.98 

1.61 

73.97 

1.94 

73.97 

2.26 

74 

75 

74.99 

1.31 

74.98 

1.64 

74.97 

1.96 

74.97 

2.29 

75 

76 

75.99 

1.33 

75.98 

1.66 

75.97 

1.99 

75.96 

2.32 

76 

77 

76.9S 

1.34 

76.98 

1.68 

76.97 

2.02 

76.96 

2.35 

>7 

78 

77.99 

1.36 

77.98 

1.70 

77.97 

2.04 

77.96 

2.38 

78 

79 

78,98 

1.38 

78.98 

1.72 

78.97 

2.07 

78.96 

2.41 

79 

80 

79.9t 

1.40 

79.98 

1.75 

79.97 

2.09 

79.96 

2.44 

80 

81 

80.9S 

1.41 

80.98 

1.77 

80.97 

2.12 

90.96 

2.47 

81 

82 

81.9< 

1.43 

81.98 

1.79 

81.97 

2.15 

81.96 

2.50 

82 

83 

82.98 

1.45 

82.98 

1.81 

82.97 

2.17 

82.96 

2.53 

83 

84 

83.99 

1.47 

83.98 

1.83 

83.97 

2.20 

83.96 

2.57 

84 

85 

84.  9i 

1.48 

84.98 

1.85 

84.97 

2.23 

84.96 

2.60 

85 

86 

85.9k 

1.50 

85.98 

1.68 

85.97 

2.25 

85.96 

2.63 

86 

87 

86.99 

1.52 

86.98 

1.90 

86.97 

2.28 

86.96 

2.66 

87 

88 

87.9£ 

1.54 

87.98 

1.92 

87.97 

2.30 

87.96 

2.69 

88 

89 

88.9E 

1.55 

88.98 

1.94 

88.97 

2.33 

88.96 

2.72 

89 

90 

89.9S 

1.57 

89.98 

1.96 

89.9" 

2.36 

89.96 

2.7o 

90 

91 

90.  9J, 

1.59 

90.98 

1.99 

fO.97 

2.3 

90.96 

2.78 

91 

92 

91.  9£ 

1.61 

91.98 

2.01 

91.97 

2.4 

91.96 

2.8 

92 

93 

£2.9C 

1.62 

92.98 

2.03 

92.97 

2.43 

92.96 

2.8 

93 

94 

93.  96 

1.64 

93.98 

2.05 

93.97 

2.4 

93.96 

2.8 

94 

95 

94.98 

1.66 

94.98 

2.07 

94.97 

2.4 

94.96 

2.9 

95 

9G 

95.99 

1.68 

96.98 

2.09 

95.97 

2.5 

95.96 

2.9 

96 

97 

96.9S 

1.69 

96.9 

2.12 

96.97 

2.5 

96.95 

2.9 

97 

98 

97.9 

1.7 

97.9 

2.1 

97.9 

2.5 

97.9o 

2.9 

98 

99 

98.9 

1.73 

98.9 

2.1 

98.9 

2.5 

98.95 

3.02 

99 

IOC 

99.9 

1.7t 

99.9 

2.1 

99.9 

2.6 

99.9S 

3.0 

100 

•4-J 

Dep 

Lat 

Dep 

Lat 

Dep 

Lat 

Dep 

Lat. 

. 

.2 

L  r            

/_ 

__  ,  ^I__[L  ^rr 

^  '  ^      

,2 

Q 

89  Deg 

88fDeg 

88iDeg 

88]Deg 

'f^. 

0 

TRAVERSE  TABLE. 


5 

2Deg. 

21  Deg 

21  Deg 

2f  Det, 

t> 

r 

Lat 

Dep 

Lat 

Dep 

Lat 

Dep 

Lat 

DC1 

to 

i 

1.00 

0.0 

1.00 

0.0 

M 

0.0 

l.OC 

0.0 

g 

2.00 

0.0 

2.00 

0.0 

2.W 

0.0 

2.0C 

0.1 

c. 

3.00 

0.10 

3.00 

0.1 

3.0( 

0.1 

3.0C 

0.1 

4 

4.00 

0.14 

4.00 

0.1 

4.CK 

0.1 

4.0C 

0.1 

, 

r 
U 

5.00 

0.1 

5.0C 

0.2 

5.0( 

0.2 

4.9S 

0.2 

5 

6 

6.00 

0.2 

6.00 

0.24 

5.9 

0.26 

5.99 

0.2 

7 

7.00 

0.24 

6.99 

0.27 

6.9 

0.3 

6.99 

0.3 

8 

7.99 

0.28 

7.99 

0.31 

7.9 

0.3 

7.99 

0.3 

8 

9 

8.99 

0.3 

8.99 

0.35 

8.98 

0.3 

8.99 

0.4 

i 

10 

9.99 

0.35 

9.99 

0.39 

9.9 

0.4 

9.99 

0.4 

10 

11 

10.99 

0.38 

10.99 

0.43 

10.9 

0.4 

10.99 

0.5 

11 

12 

11.99 

0.42 

11.99 

0.47 

11.9 

0.5 

11.99 

0.5 

12 

13 

12.99 

0.45 

12.99 

0.51 

12.9 

0.5 

12.99 

0.6 

IS 

14 

13.99 

0.49 

13.99 

0.55 

13.9 

0.6 

13.98 

0.6 

14 

15 

14.99 

0.52 

14.99 

0.59 

14.9 

0.6 

14.98 

0.7 

15 

16 

15.99 

0.56 

15.99 

0.63 

15.9 

0.70 

15.18 

0.7 

16 

17 

16.99 

0.59 

16.99 

0.67 

16.9 

0.74 

16.98 

0.8 

17 

18 

17.99 

0.63 

17.99 

0.71 

17.9 

0.79 

17.98 

0.8 

18 

19 

18.99 

0.66 

18.99 

0.75 

18.9 

0.83 

18.98 

0.9 

19 

20 

19.99 

0.70 

19.98 

0.79 

19.9 

0.87 

19.98 

0.9 

20 

21 

20.99 

0.73 

20.98 

0.82 

20.98 

0.92 

20.98 

1.0 

21 

22 

21.99 

0.77 

21.98 

0.86 

21.98 

0.96 

21.97 

1.06 

22 

23 

22.99 

0.80 

22.98 

0.90 

22,98 

1.00 

22.97 

1.10 

23 

24 

23.99 

0.84 

23.98 

0.94 

23.98 

1.05 

23.97 

1.15 

24 

25 

24.98 

0.87 

24.98 

0.98 

24.98 

1.09 

24.97 

1.20 

"5 

26 

25.98 

0.91 

25.98 

1.02 

25.98 

1.13 

25.97 

1.25 

26 

27 

26.98 

0.94 

26.98 

1.06 

6.97 

1.18 

26.97 

1.30 

27 

28 

27.98 

0.98 

27.98 

1.10 

7.97 

1.22 

27.97 

1.34 

28 

29 

28.98 

1.01 

28.98 

1.14 

8.97 

1.26 

28.97 

1.39 

29 

30 

29.98 

1.05 

29.98 

1.18 

9.97 

1.31 

29.97 

1.44 

30 

31 

30.98 

1.08 

30.98 

1.22 

0.97 

1.35 

30.96 

1.49 

31 

3231.98 

1.12 

31.98 

1.26 

1.97 

1.40 

1.96 

1.54 

32 

3332.98 

1.15 

32.97 

1.30 

2.97 

1.44 

2.96 

1.58 

33 

34  33.98 

1.19 

33.97 

1.33 

3.97 

1.48 

3.96 

1.63 

34 

35 

34.98 

1.22 

34.97 

1.37 

4.97 

1.53 

4.96 

1.68 

35 

36 

35.98 

1.26 

35.97 

1.41 

5.97 

1.57 

5.96 

1.73 

36 

37 

36.98 

1.29 

36.97 

1.45 

6.96 

1.61 

36.96 

1.78 

37 

38 

37.98 

1.33 

37.97 

1.49 

7.96 

1.66 

7.96 

1.82 

38 

39 

38.98 

1.36 

38.97 

1.53 

8.96 

1.70 

8.96 

1.87 

39 

40 

39.98 

1.40 

39.97 

1.57 

9.96 

1.75 

9.95 

1.92 

4<) 

41 

40.98 

1.43 

40.97 

1.61 

40.96 

1,77 

0.95 

1.97 

41 

42 

41.97 

1.47 

41.97 

1.65 

1.96 

1.83 

1.95 

2.02 

42 

43 

42.97 

1.50 

2.97 

1.69 

2.96 

1.88 

2.95 

2.0C 

43 

44 

43.97 

1.54 

3.97 

1.73 

3.96 

1.92 

43.95 

2.11 

44 

45 

44.97 

1.57 

4.97 

1.77 

4.96 

1.96 

44.95 

2.16 

45 

46 

45.9% 

1.61 

45.96 

1.81 

5.96 

2.01 

5.95 

2.21 

46 

47 

46.97 

1.64 

6.96 

1.85 

6.96 

2.05 

6.95 

2.25 

47 

48 

47.97 

1  68 

7.96 

1.88 

7.95 

2.09 

7.95 

2.30 

48 

49 

48.97 

1.71 

8.96 

1.92 

8.95 

2.14 

8.M 

2.35 

49 

50 

49.97 

1.74 

9.96 

1.96 

9.95 

2.18 

9.94 

2.40 

50 

tg 

Dep. 

Lat. 

Dep. 

Lat. 

ep. 

Lat. 

ep. 

Lat. 

c 

Q 

88  Deg. 

87fDeg. 

7iDeg. 

TJ: 

>eg. 

5 

TRAVERSE  TABLE. 


43 


5 

2  Deg. 

21  Deg 

2i  Deg. 

2|  Deg. 

g 

c" 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

35 

rt- 

51 

50.97 

.78 

0.96 

2.00 

0.95 

2.22 

0.94 

2.45 

51 

52  51.97 
53J52.97 
54!53.97 

.81 
.85 

.88 

1.96 
2.96 
3.96 

2.04 
2.08 
2.12 

1.95 
2.95 
53.95 

2.27 
2.31 
2.36 

1.94 
2.94 
3.94 

2.50 
2.54 
2.59 

52 
53 
54 

55  54.97 

.92 

4.96 

2.16 

54.95 

2.40 

4.94 

2.64 

55 

56155.97 

.95 

5.96 

2.20 

55.95 

2.44 

55.94 

2.69 

56 

5756.97 

.99 

6.96 

2.24 

56.95 

2.49 

56.93 

2.73 

57 

5857.96 

2.02 

7.96 

2.28 

57.94 

2.53 

57.93 

2.78 

58 

59 

58.96 

2.06 

8.95 

2.32 

58.94 

2.57 

58.93 

2.83 

59 

60 

59.96 

2.09 

9.95 

2.36 

59.94 

2.62 

59.93 

2.88 

60 

61 

60.96 

2.13 

0.95 

2.39 

60.94 

2.66 

60.93 

2.93 

61 

62 

61.96 

2.16 

bl.95 

2.43 

61.94 

2.70 

61.93 

2.97 

62 

63 

62.96 

2.20 

62.95 

2.47 

62.94 

2.75 

62.93 

3.02 

63 

64 

63.96 

2.23 

63.95 

2.51 

63.94 

2.79 

63.93 

3.07 

64 

65 

64.96 

2.27 

64.95 

2.55 

64.94 

2.84 

64.93 

3.12 

65 

66 

65.96 

2.30 

65.95 

2.59 

65.94 

2.88 

65.92 

3.17 

66 

67 

66.96 

2.34 

66.95 

2.63 

66.94 

2.92 

66.92 

3.21 

67 

68 

67.96 

2.37 

67.95 

2.67 

67.94 

2.97 

67.92 

3.26 

68 

69 

68.96 

2.41 

68.95 

2.71 

68.93 

3.01 

68.92 

3.31 

69 

70 

69.96 

2.44 

69.95 

2,75 

69.93 

3.05 

69.92 

3.36 

70 

71 

70.96 

2.48 

"0.95 

2.79 

70.93 

3.10 

70.92 

3.41 

71 

72 

71.96 

2.51 

71.94 

2.83 

71.93 

3.14 

71.92 

3.45 

72 

73 

72.96 

2.55 

72.94 

2.87 

72.93 

3.18 

72.92 

3.50 

73 

74 

73.95 

2.58 

73.94 

2.91 

73.93 

3.23 

73.91 

3.55 

74 

75 

74.95 

2.62 

74.94 

2.94 

74.93 

3.27 

74.91 

3.60 

75 

76 

75.95 

2.65 

75.94 

2.98 

75.93 

3.31 

75.91 

3.65 

76 

77 

76.95 

2.69 

76.94 

3.02 

76.93 

3.36 

76.91 

3.70 

77 

78 

77.95 

2.72 

77.94 

3.06 

77.93 

3.40 

77.91 

3.74 

78 

79 

78.95 

2.76 

78.94 

3.10 

78.92 

3.45 

78.91 

3.79 

79 

80 

79.95 

2.79 

79.94 

3.14 

79.92 

3.49 

79.91 

3.84 

80 

81 

80.95 

2.83 

80.94 

3.18 

80,92 

3.53 

80.91 

3.89 

81 

82 

81.95 

2.86 

81.94 

3.22 

81.92 

3.58 

81.91 

8.93 

82 

83 

82.95 

2.90 

82.94 

3.26 

82.92 

3.62 

82.90 

3.98 

83 

84 

83.95 

2.93 

83.94 

3.30 

83.92 

3.66 

83.90 

4.03 

84 

85 

84.95 

2.971 

84.93 

3.34 

84.92 

3.71 

84.90 

4.08 

83 

86 

85.95 

3.00 

85.93 

3.38 

85.9L 

3.75 

85.90 

4.13 

8S 

87 

86.95 

3.04 

86.93 

3.42 

86.92 

3.79 

86.90 

4.17 

87 

88 

87.95 

3.07 

87.93 

3,45 

87.92 

3.84 

87.90 

4.22 

88 

89 

88.95 

3.11 

88.93 

3.49 

88.92 

3.88 

88.90 

4.27 

89 

80 

89.95 

3.14 

89.93 

3.53 

89.91 

3.93 

89.90 

4.32 

90 

91 

90.95 

3.18 

90.93 

3.57 

90.91 

3.97 

90.90 

4.3" 

91 

92 

91.94 

3.21 

91.93 

3.61 

91.91 

4.01 

91.89 

4.41 

92 

93 

92.94 

3.25 

92.93   3.65 

92.91 

4.06 

92.89 

4.4f 

93 

94 

93.94 

3.28 

93.93    3.69 

93.9 

4.10 

93.89 

4.51 

94 

95 

94.94 

3.32 

94.93    3.73 

94.91 

4.14 

94.89 

4.56 

95 

96 

95,94 

3.3 

95.93    3.77 

95.9 

4.19 

95.89 

4.61 

96 

9" 

96.94 

3.3 

96.93;  3.8 

96.9 

4.23 

96.89 

4.65 

97 

9S 

97.94 

3.4 

97.92!  3.85 

97.9 

4.27 

97.89 

4.70 

98 

9< 

98.94 

3.4 

98,92'  3.89 

98.9 

4.32 

98.89 

4.75 

99 

IOC 

99.94 

3.4 

99.92J  3.93 

i 

99.9 

4.36 

99.88 

4.8C 

100 

ts 

Dep 

Lat 

Dep.  Lat 

Dep 

Lat 

Dep. 

Lat 

-s 

S 

88  Dee 

87-|Deg 

87£Deg 

87iDeg 

5 

44 


TRAVERSE  TABLE. 


o 
w* 

3Deg. 

3i  Deg. 

3*  Deg. 

3f  Deg. 

g 
» 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.jDep. 

Lat.l 

Dep. 

i 

1.00 

0.05 

1.00 

0.06 

1.00 

0.06 

1.00 

0.06 

1 

2 

2.00 

0.10 

2.00 

0.11 

2.00 

0.12 

2.00 

0.13 

2 

3 

3.00 

0.16 

3.00 

0.17 

2.99 

0.18 

2.99 

0.20 

3 

4 

3.99 

0.21 

3.99 

0.23 

3.99 

0.24 

3.99 

0.26 

4 

5 

4.99 

0.26 

4.99 

0.28 

4.99 

0.31 

4.99 

0.33 

5 

6 

5.99 

0.31 

5.99 

0.34 

5.99 

0.37 

5.99 

0.39 

6 

7 

6.99 

0.37 

6.99 

0.40 

6.99 

0.43 

6.99 

0.46 

7 

8 

7.99 

0.42 

7.99 

0.45 

7.99 

0.49 

7.98 

0.52 

8 

9 

8.99 

0.47 

8.98 

0.51 

8.98 

0.55 

8.98 

0.59 

g 

10 

9.99 

0.52 

9.98 

0.57 

9.98 

0.61 

9.98 

0.65 

10 

11 

10.98 

0.58 

10.98 

0.62 

10.98 

0.67 

10.98 

0.72 

11 

12 

11.98 

0.63 

11.98 

0.68 

11.98 

0.73 

11.97 

0.78 

12 

13 

12.98 

0.68 

12.98 

0.73 

12.98 

0.79 

12.97 

0.85 

13 

14 

13.98 

0.73 

13.98 

0.79 

13.97 

0.85 

13.97 

0.92 

14 

15 

14.98 

0.79 

14.98 

0.85 

14.97 

0.92 

14.97 

0.98 

15 

16 

15.98 

0.84 

15.97 

0.91 

15.97 

0.98 

15.97 

1.05 

16 

17 

16.98 

0.89 

16.97 

0.96 

16.97 

1.04 

16.96 

1.11 

17 

18 

17.98 

0.94 

17.97 

.02 

17.97 

1.10 

17.96 

1.18 

18 

19 

18.98 

0.99 

18.97 

.08 

18.96 

.16 

18.96 

1.24 

19 

20 

19.97 

1.05 

19.97 

.13 

19.96 

.22 

19.96 

1.31 

20 

21 

20.97 

1.10 

20.97 

.19 

20.96 

.28 

20.96 

1.37 

21 

22 

21.97 

1.15 

21.96 

.25 

21.96 

.34 

21.95 

1.44 

22 

23 

22.97 

1.20 

22.96 

.30 

£2.96 

.40 

22.95 

1.50 

2£ 

24 

23.97 

1.26 

23.96 

.36 

23.96 

.47 

23.95 

1.57 

24 

25 

24.97 

1.31 

24.96 

.42 

24.95 

.53 

24.95 

1.64 

25 

26 

25.96 

1.36 

25.96 

.47 

25.95 

.59 

25.94 

1.70 

26 

27 

26.96 

1.41 

26.S6 

.53 

26.95 

.65 

26.94 

1.77 

27 

28 

27.96 

1.47 

27.95 

.59 

27.95 

.71 

27.94 

1.83 

28 

29 

28.96 

1.52 

28.95 

.64 

28.95 

.77 

28.94 

1.90 

2f 

30 

29.96 

1.57 

29.95 

.70 

29.94 

.83 

29.94 

1.96 

30 

31 

30.96 

1.62 

30.95 

.76 

30.94 

.89 

30.93 

2.03 

31 

32 

31.96 

1.67 

31.95 

.81 

31.94 

.95 

31.93 

2.09 

32 

33 

32.95 

1.73 

32.95 

.87 

32.94 

2.01 

32.93 

2.16 

33 

34 

33.95 

1.78 

33.95 

.93 

33.94 

2.08 

33.93 

2.22 

34 

35 

34.95 

1.83 

34.94 

1.98 

34.93 

2.14 

34.92 

2.29 

35 

36 

35.95 

1.88 

35.94 

2.04 

35.93 

2.20 

35.92 

2.35 

36 

37 

36.95 

1.94 

36.94 

2.10 

36.93 

2.26 

36.92 

2.42 

37 

38  37.95 

1.99 

37.94 

2.15 

37.93 

2.32 

37.92 

2.49 

38 

39 

38.95 

2.04 

38.94 

2.21 

38.93 

2.38 

38.92 

2.55 

39 

40 

39.95 

2.09 

39.94 

2.27 

39.93 

2.44 

39.91 

2.62 

40 

41 

40.94 

2.15 

40.93 

2.32 

40.92 

2.50 

40.91 

2.68 

41 

42 

41.94 

2.20 

41.93 

2.38 

41.92 

2.56 

41.91 

2.75 

42 

43 

42.94 

2.25 

42.93 

2.44 

42.92 

2.63 

42.91 

2.81 

43 

44 

43.94 

2.30 

43.93 

2.49 

43.92 

2.69 

43.91 

2.88 

44 

45 

44.94 

2.36 

44.93 

2.55 

44.92 

2.75 

44.90 

2.94 

45 

46 

45.94 

2.41 

45.93 

2.61 

45.91 

2.81 

45.90 

3.01 

46 

47 

46.94 

2.46 

46.92 

2.66 

46.91 

2.87 

46.90 

3.07 

47 

48 

47.93 

2.51 

47.92 

2.72 

47.91 

2.93 

47.90 

3.14 

48 

49 

48.93 

2.56 

48.92 

2.78 

48.91 

2.99 

48.90 

3.20 

49 

50 

49.93 

2.62 

49.92 

2.83 

49.91 

3.05 

49.89 

3.27 

50 

s 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

"eg 

5 

87  Deg. 

86$Deg. 

86iDeg. 

86iDeg. 

TRAVERSE  TABLE. 


45 


0'  3Deg.  j|3iDeg. 

I  <H  Peg. 

3|  Deg. 

5 

?*   Lat.  Dep.    Lat.|Dep.|  Lat. 

Dep. 

Lat. 

Dep. 

nr>' 

r- 

51  50.93   2.67  J50.92!  2.89 

50.90 

3.11 

50.89 

3.34!  51 

52  51.93 

2.72  51.921  2.95 

151.90 

3.17 

51.89   3.40   52 

5352.93 
54;53.93 

2.77i52.9li  3.00 
2.83,  53.91  1  3.06 

52.90 
53.90 

3.24 
3.30; 

52.89   3.47   53 
53.88   3.53   54 

55|54.92 

2.88  '54.911  3.12 

54.90 

3.36 

54.88 

3.60:  55 

56|55.92 

2.93  55.91    3.17 

55.90 

3.42;  55.88 

3.66;  56 

5756.92 

2.98156.91    3.23 

56.89 

3.48: 

56.88 

3.73   57 

5857.92   3.04157.91 

3.29 

57.89 

3.54! 

57.88 

3.79 

58 

5958.92   3.0958.91 

3.34 

58.89 

3.60 

58.87 

3.86   59 

6059.92 

3.14  59.90 

3.40 

59.89 

3,66|j59.87 

3.92   CO 

61  60.92J  3.19  60.90 

3.46 

60.89 

3.72 

60.87 

3.99   61 

6261.92   3.24|  61.90 

3.51 

61.88 

3.79 

61.87 

4.05   62 

63162.91;  3.30162.90 

3.57 

62.88 

3.85 

62.87 

4.12    63 

6463.91    3.35163.90 

3.63 

63.88 

3.91 

63.86 

4.19    64 

65,64.91'  3.40,64.90 

3.69 

64.88 

3.97 

64.86 

4.25   65 

6665.91!  3.451  65.89 

3.74 

65.88 

4.03 

65.86 

4.32    66 

67  66.911  3.51  i66.89 

3.80 

66.88 

4.09 

66.86 

4.38!  67 

6867.91   3.56  '67.89 

3.86 

67.87 

4.15 

67.85 

4.45i  68 

6968.91    3.61168.89 

3.9l!  168.87 

4.21 

68.85 

4.51!  69 

70(69,90   3,6669.89 

3.97 

i69.87 

4.27 

69.85 

4.58 

70 

7l!70.90  3.72170.89 

4.03 

170.87 

4.33 

70.85 

4.64 

71 

72;71.90   3.77  71.88 

4.08 

!71.87 

4.40 

71.85 

4.71 

72 

73,72.90  3.82'|72.88 

4.14 

72.86 

4.46 

72.84 

4.77 

73 

7473.90!  3.87173.88 

4.20 

,73.86 

4.52 

73.84 

4.84 

74 

75  74.90,  3.93  174.88 

4.25 

74.86 

4.58 

74.84 

4.91 

75 

76,75.90   3.98  75.  8§ 

4.31 

175.86 

4.64 

75.84 

4.97 

76 

7776.89'  4.03;76.S8 

4.37 

,76.86 

4.70 

76.84 

5.04    77 

7877.89!  4.08,177.87 

4.42 

77:85 

4.76 

77.83 

5.10J  78 

7978.89   4.13  78.87 
8079.89   4.  191  79.87 

L_  I  

4.48 
4.54 

78.85 

79.85 

4.82 
4.88 

78.83 
79.83 

5.17    79 

5.23J  80 

8180.89 

4.24! 

80.87 

4.59!  80.85 

4.94 

80.83 

5.30   81 

8281.89 

4.29| 

81.87 

4.65 

81.85 

5.0li81.82 

5.36   82 

83  82.89 

4.34 

82.87 

4.71 

182.85 

5.07 

82.62 

5.43    83 

84  83.88 

4.40 

83.86 

4.76 

!83.84 

5.13  183.82 

5.49    84 

8584.88 

4.45 

84.86 

4.82;  184.84 

5.  19  [84.  82 

5.56    85 

8685.88 

4.50 

85.86 

4.88 

85.84 

5.25 

85.82 

5.62    86 

87  86.88 

4.55: 

86.86 

4.93 

86.  94 

5.31 

86.81 

5.69 

87 

8887.88 

4.61 

87.86 

4.99 

87.84 

5.37 

87.81 

5.76 

88 

89  88.88 

4.68 

88.86 

5.05 

88.83 

5.43 

88.81 

5.82   89 

9089.88 

4.71; 

89.86 

6.10 

:89.83 

5.49 

89.81 

5.89   SO 



' 





91  90.88 

4.76 

90.85 

5.16(90.83 

5.56! 

90.81 

5.95    Gl 

92  91.87 

4.81 

91.85 

5.22!  191.83 

5.62 

91.80 

6.02   92 

9392.87 
94  93.87 

4.87 
4.92 

92.85 
93.85 

5.27^92.83 
5.33!  93.82 

5.68 
5.74 

92.80 
93.80 

6.08 
6.15 

93 
94 

95  94.87 

4.97 

94.85 

5.39 

94.62 

5.80 

94.80 

6.21 

95 

96  95.87 

5.02 

95.85 

5.44  195.82 

5.88 

95.79 

6.28 

96 

97  96.87 

5.08j  96.84 

5.50i96.82 

5.92 

96.79 

6.34 

a? 

98  97.87 

5.13  97.84   5.56';97.82 

5.98 

97.79 

6.41 

9S 

99  98.86 

5.18  98.84   5.61 

!98.&2 

6.04  '98.79 

6.47 

99 

10099.86 

5,23 

99.84 

5.67 

J99.81 

6.10 

99.79 

6.64 

100 

«  Dep< 

Lat. 

Dep. 

~Lat~ 

Dep. 

nr 

Dep. 

Lat. 

CO 

5  1  87  Peg. 

86*  Deg.li86iBeg.|i86£Deg.  5 

11 


46 


TRAVERSE  TABLE. 


g!  4  Deg. 

41  Deg. 

41  Deg. 

4f  Deg. 

e 

r  |  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.    Lat.  JDep. 

pi 

1    1.00  0.07     1.00 

0.07| 

1.00 

0.08    1.00  0.03 

1 

2  2.00 

0.141  1.99 

0.15 

1.99 

0.16    1.99   0.17 

2 

3   2.99 

0.21     2.99 

0.22, 

2.99 

0.24    2.99    0.25 

3 

4   3.99 

0.28    3.99 

0.30| 

3.99 

0.31    3.98   0.33 

4 

5   4.99 

0.35    4.99 

0.37 

4.98 

0.39  !  4.98   0.41 

5 

6   5.99J  0.42 

5.98 

0.44 

5.98 

0.47 

5.98   0.50 

6 

7   6.981  0.49 

6.98 

0.52J 

6.98 

0.55 

6.97 

0.58 

7 

'    8|  7.98 

0.56 

7.98 

0.59 

7.98 

0.63 

7.97 

0.66 

8 

9   8.98 

0.63 

8.98 

0.67 

8.97J  0.71 

8.97 

0.75 

9 

IOJ  9.98 

0.70 

9.97 

la 

9.97 

0.78 

9.97 

0.83 

10 

11  10.97J  0.77 

10.97 

0.82 

10.97 

0.86 

10.96 

0.91 

11 

12|ll.97 

0.84  11.97 

0.89|ill.96i  0.94  11.96 

0.99 

12 

13  12.97 

0.91  12.96 

0.961142.96 

.0212.96     .08 

13 

1413.97 

0.98  13.96 

1.04 

13.96 

.10  13.95     .16 

14 

15!  14.96    1.05  14.96 

l.ll) 

14.95 

.18 

14.95     .24 

15 

16  15.96 

1.12  15.96 

1.191115.95      .26 

15.95 

.32 

16 

1716.96 

1.19  16.95 

1.26!  16.96     .33 

16.94 

.41 

17 

18  17.96 

1.26  17.95 

1.33 

17.94 

.41 

17.94     .49 

18 

19  18.95    1.33  18.95 

1.40r 

18.94 

.49 

18.93 

.57 

19 

20,19.95!  1.40  19.95 
2l'20.95    1.4620.94 

1.48)19.94 
1.56  J20.94 

.57 
.65 

19.93 
^20.93 

.66 

20 
21 

.74 

2221.95J  1-53  21.94 

1.63 

21.93 

.73 

|21.92 

.82   22 

2322.941  1.60  22.94 

1.70|,  22.93 

.80 

22.92 

.90   23 

2423.941  1.67;  23.93 

1.78 

23.93 

.88 

23.92 

.99   24 

2524.941  1.74  24.93 

1.85 

24.92 

.96 

24.91 

2.07   25 

2625.94    1.81  25.93 

1.93 

25.92 

2.04  125.91 

2.15'  26 

2726.93    1.88  26.93 

2.00  26.92 

2.12  26.91 

2.24!  27 

28  27.93 

1.95  27.92 

2.08; 

27.91 

2.20  127.90 

2.32   28 

2928.93 

2.02|:28.92 

2.15 

28.91 

2.28128.90 

2.40   29 

30,29.93 

2.09,;29.92 

2.22 

29.91 

2.35  J29.90 

2.48   30 

3130.92 

2.16  30.91 

2.30  30.90 

2.43!30.89 

2.57   31 

3231.92 

2.23  31.91 

2.37 

31.90 

2.5t31.89 

2.65   32 

33  32.92 

2.30  ;32.91 

2.45 

32.90 

2.59.I32.89 

2.73   33 

34  33.92 

2.37 

33.91 

2.52 

33.90 

2.67  33.88   2.82   34 

3534.91 

2.44  !34.90 

2.59! 

34.89 

2.75  34.88   2.90   35 

3635.91 

2.511:35.90 

2.67,35.69 

2.82  35.88   2.98 

36 

3736.91 

2.58  36.90 

2.74 

36.89 

2.90  '36.87   3.06 

37 

3837.91 

2.65  :37.90 

2.82  '37.88 

2.98  37.87    3.15 

38 

3938.90 

2.72|;38.89 

2.89 

38.88 

3.06 

38.87   3.23 

39 

4039.90 

2.79  39.89 

2.95; 

39.8SJ  3.14 

39.86i  3.31 

40 

"4140.90 

2.86J  40.89 

3.04!  140.871  3.22 

40.86   3.40 

41 

4241.90 

2.93  41.88 

3.11 

41.87 

3.30  41.861  3.48 

42 

43:42.90 
44'43.69 

3.00  42.88 
3.07  43.88 

3.19 
3.26 

42.87   3.37J42.85 
43.86   3.45  (43.85 

3.56 
3.64 

43 
44 

4544.89   3.1444.88 

3.33 

44.86   3.53 

44.85 

3.731  45 

46  45.89 

3.21  45.87 

3.41 

45.86 

3.61  45.84 

3.81   46 

47146.89 
4847.88 

3.28  46.87 
3.35  47.87 

3.48;46.86 
3.56  i47.85 

3.69  146.84 
3.771  47.84 

3.89   47 
3.97   48 

4948.88 

3.42  48.87 

3.6348.85 

3.84148.83 

4.06 

49 

5049.88 

3.49 

49.86 

3.71 

49.85 

3.92 

49.83 

4.14 

50 

*2  Dep. 

to    . 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

tn- 

5   86  Deg. 

86£DegJ 

85iDeg. 

SSiDe^A 

TRAVERSE  TABLE. 


47 


g!  4  Deg.     4]  Deg.l  4J  Deg.  1  4J  Deg.i  ^ 

rial 

Dep.    Lat. 

Dep. 

Lat.  Dep.  |  Lat."Dep.;  r 

51!50.88 

3.56  50.86 

3.78;  50.841  4.0o!>50.82   4.22!  51 

5251.87 

3.63  51.86 

3.85!51.84   4.08!51.82|  4.31    52 

5352.87 

3.70  52.85 

3.93152.84   4.16  ;52.82i  4.S9J  53 

5453.87 

3.77  53.85 

4.00|i53.83   4.24  53.81!  4.4?!  54 

55  54.87 

3.84  54.85 

4.08;  54.83   4.32,54.81    4-55!  55 

5655.86 

3.91  55.85 

4.15155.83      .39 

55.811  4.641  56 

57,56.86 

3.98i  56.84 

4.22  56.82'     .47156.80   4.72;  57 

58  57.86 

4.05  57.84 

4.30'  57.82!     .55157.80   4.80!  58 

59  58.86 

4.12  58.84 

4.3758.82     .6358.80,4.89159 

6059.85 

4.19  159.84 

4.45|59.82i     .71159.79   4.97   60 

61  60.85 

4.26  60.83 

4.52  60.81    4.79:!60.79!  5.05'  61 

6261.85 

4.32  61.83 

4.59,61.81    4.86  61.79    5.13;  62 

6362.85 

4.39  62.83 

4.67  62.811  4.94  62.78   5.22j  63 

6463.84 

4.46!63.82 

4.74  63.80'  5.02  63.78   5.30   64 

6564.84 

4.53  64.82 

4.82l64.80!  5.10!64.78!  5.38   65 

6665.84 

4.60  65.82 

4.89  65.80,  5.18  65.77!  5.47!  66 

67'66.84 

4.67  66.82 

4.97:  66.79;  5.26  66.77!  5.551  67 

68  67.83 

4.74  67.81 

5.04167.79    5.34  67.77!  5.63    68 

6968.83 

4.81  68.81 

5.11  S8.79   5.41  68.76    5.71,  69 

7069.83 

4.88  69.81 

5.19 

69.78|  5.49  69.76   5.80'  .70 

7170.83 

4.95  70.80 

5.26 

70.78   5.57 

70.76;  5.88!  71 

7271.82 

5.02  71.80 

5.34 

71.78   5.65  171.  75^5.96    72 

73  72.82 

5.09  72.80 

5.41 

72.77    5.73  72.75    6.04!  73 

74  73.82 

5.16  73.80 

5.48 

73.77   5.  81'  73.75   6.13!  74 

75  74.82 

5.23  74.79 

5.56 

74.77   5.88J  74.74   6.21    75 

76  75.81 

5-30  75.79 

5.63 

75.77   5.96  75.74   6.29    76 

77  76.81 

5.37  76.79 

5.71 

76.76   6.04 

76.74   6.38    77 

7877.81 

5.44  77.79 

5.78 

77.76   6.12 

77.73,  6.46    78 

79  78.81 

5.51  78.78 

5.85 

78.76   6.20 

78.73   6.54   79 

80  79.81 

5.58  79.78 

5.93 

79.75   6.28 

79.73   6.62'  80 

81  80.80   5.65  80.78 

6.00 

80.75   6.36 

80.72'  6.71S  81 

828^.80 

5.72  fll.78 

6.08  81.75   6.43  81.72   6.79    82 

83  82.80 

5.79  82.77 

6.15|  82.74   6.511182.71;  6.87    83 

8483.80 

5.86  83.77 

6.23!  83.74   6.59!  83.7L  6.96!  84 

85  84.79 

5.93  84.77 

6.30|  84.74   6.67l!84.7li  7.04i  85 

86  85.79 

6.00  85.76 

6.37 

85.73   6.75  |85.70'  7.12    86 

87  86.79 

6.07  186.76 

6.45 

86.73   6.83  86.70    7.20:  87 

88J87.79 

6.14  87.76 

6.52 

87.73   6.90!  87.70)  7.29;  88 

8988.78 

6.21  !88.76 

6.60 

88.73   6.98>!88.70   7.37;  89 

90.89.78 

6.28J  89.76 

6.67 

89.72   7.06  89.69    7.45!  90 

91  90.78 

6.35-90.75 

6.  74!  90.72    7.  141  90.69    7.54    91 

9291.78 

6'.42  9l'.75 

6.82|  91.72   7.22  91.6&  7.62[  92 

9392.77 

6.49,92.74 

.6.89  92.71    7.30 

92.681  7.70!  93 

94'93.77 

6.56  193.74 

6.97'93.71    7.38 

93,68!  7.78!  94 

9594.77 

6.631  J94.74 

7.04,54.71    7.45 

94.67i  7.87]  95 

96|95.77 

6.70  95.74 

7.11  ;95.70   7.53 

95.67;  7.95J  96 

9796.76 

6.77  96.73 

7.19JJ96.70   7.61 

96.67!  8.03    97 

98  97.76 

6.84  97.73 

7.26!  i97.70    7.69 

;97.66    8.12!  98 

9998.76 

6.91'|98.73 

7.34J  ;98.69   7.77 

98.661  8.20    99 

100J99.76 

6.98:|99.73 

7.41J  |99.69   7.85 

99.66!  8.28  100 

+}  Dep.l  Lat.l  Dep. 

Lat.  iDep.   Lat. 

Dep.|  Lat.j^J 

02     , 

<    &} 

3    86  DegJ!86'Deg.  85^  Deg. 

86*  Deg,  |O 

48 


TRAVERSE  TABLE. 


5 

5  Deg.  ,[64  Deg.   5J  Deg.;j 

5£  Deg. 

g 

5* 

•   '"   ••   ••• 

Lat. 

Dep. 

Lat.  Dep.  Ij  Lat. 

^±ii. 

Lat." 

Oep. 

83" 

-  — 

1.00 

0.09 

1.00  0.09 

1.00 

0.10 

0.99 

0.10     1 

2 

1.99 

o.n;  1,99  o.is;  1.99 

0.19! 

1.99 

0.20 

^2 

3 

2.99 

0.26    2.99   0.27    2.99 

0.29|| 

2.98 

0.30 

g 

4 

3.98 

0.35    3,98,  0.37  i  3.98 

0.38 

3.98   0.40 

4 

5 

4,98 

0.44 

4.98  0.46;   4.98 

0.48 

4.97 

0.50 

t 

6 

5,98 

0.52 

5,97   0.55    5,97 

0.58 

5.97 

0.60 

\ 

7 

6.97 

0.61! 

6,97!  0.64    6.97 

0.671 

6.96 

0.70 

*t 

8 

7.97 

0.70, 

7,97  0.73;  7.96 

0.76! 

7.96 

0.80     8 

9 

8.97 

0.78 

8.96   0.82J  8.96 

0.86! 

8.95 

0.90     9 

a 

9.96 

0.87 

9.96 

0.92 

9.95 

0.961 

; 

9.95 

1.00!  10 

lli  10.96 
1211.95 

0.96 
1.05 

10,95 
11.95 

l.Olj  110.95 
1.10  11.94 

1.05! 
1.15 

10.94 
11.94 

i.ioj    i 

1.2Qi     2 

13|12.95 

1.13 

12.951  1.19  12.94 

1.25! 

12.93 

1.30!     3 

1413.95 

1.22 

13.941  1.28  13.94 

1.34 

13.93 

1.40,     4 

15 

14.94 

1.31 

14.94]     .37  14.93 

1.44 

14.92 

1.50     5 

1615.94 

1.39 

15.931     .46,15.93 

1.53 

15.92 

1.60     6 

17 

16.94 

1.48 

16.93      .56  16.92 

1.63 

16.91 

1.70     7 

1817.93 

1.57 

17.92 

.65  17.92 

1.73 

17.91 

1.80     8 

19  18.93 

1.66 

18.92     .U  18.91 

1.82, 

18.90 

1.90;       9 

2019.92 

1.74 

19.92    1.83 

19.91 

,1.92! 

19.90 

2.00,  20 

"2120.92 

1.83 

20.91 

1.92 

20.90 

2.01! 

20.89 

2.10   21 

2221.92 

1.92 

21.91   2.01 

21.90 

2.11 

21.89 

2.20   22 

23  22.91  1  2.00 

22.90  2.10 

22.89 

2.20 

22.88 

2.30   23 

2423.91!  2.09 

23.90 

2.20 

23.89 

2.30 

23.88 

2.401  24 

3524.90   2.18  24.90  2.29 

24.88 

.2.40 

24.87 

2.50,  25 

2625.90  2.27125.89  2.38 

25.88 

2.49; 

25.87 

2.60,  26 

•2726.90  2.35126.89  2.47 

26.88 

2.59 

26.86 

2.711  27 

28,27.  89i  2.44  27.88   2.56 

27.87 

2.68, 

27.86 

2.81    28 

2928.89'  2.53 

28.88;  2.65 

28.87 

2.78 

28.85 

2.91    29 

3029.89   2.61|29.87 

2.75 

29.86 

2.88 

29.85 

3.01    30 

1! 

1 

,30.84 

Sl'30.88   2.70'S0.87 

2.84 

30.86 

2.97' 

3.1ll  31 

32:31.88   2.79  31.87 

2.93 

31.85 

3.07: 

31.84 

3.21   32 

3332.87!  2.88;  32.86   3.02  32.85 

3.16 

32.83 

3.31    33 

3433.87   2.96  33.86   3.11  33.84 

3.26 

33.83 

3.41    34 

35  34.87   3.05!  34.85   3.20  34.84 

3.35 

34.82 

3.51 

35 

3635.86  3.14135.85   3.29  35.83 

3.45 

35.82 

3.61 

36 

37J36.86   3.22 

36.841  3.39  36.83 

3.55  36.81 

3.71 

37 

38'37.86   3.31 

•37.84 

3.48  37.83 

3.64  37.81 

3.81 

38 

39  38.85   3.40 

138.84 

3.  57!  38.  82 

3.74  38.80 

3.91 

39 

40J39.85J  3.49 

J39.83 

3.  66  '39.  82 

3.83 

39.80 

4.01 

40 

4140.84   3.57 

40.83 

3.75:40.8 

3.93 

'40.79 

4.11 

41 

4241.84   3.66 

41.82 

3.84  ;41.8 

4.03 

41.79 

4.21 

42 

43J42.84   3.75|42.82 
44,43.83   3.83!  143.82 

3.93  42.80 
4.03|43.80 

4.12;42.78 
4.22  '43.  78 

4.31 
4.41 

43 
44 

4544.83 

S.92!44.81 

4;12  144.79 

4.31  44.77 

4.51 

45 

4645.82 

4.0li  45.81 

4.21  145.79 

4.41  45.77 

4.61 

46 

47  46.82 

4.10 

46.80 

4.30 

46.78 

4.50  46.76 

4.71 

47 

4847.82 

4.18 

47.80 

4.39 

47.7S 

4.60|  47.76 

4.81 

48 

49  48.81 

4.27 

48.79 

4.48 

48.77 

4.70 

148.75 

4.91 

49 

5( 

)  49.81 

4.36 

49.79 

4.58 

49.77 

4.79 

49.75 

5.01 

50 

In 

Dcp 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

.Lat. 

« 

S 

85  Deg. 

84£Deg. 

S4iDeg. 

84  \  Deg. 

5 

TRAVERSE  TABLE. 


49 


F 

5  Deg. 

5iDeg. 

51  Deg. 

bil 

Lat. 

Jeg. 
Dep. 

C 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

ft 

51 

50.81 

4.44 

0.79 

4.67 

50.77 

489 

50.74 

5.11 

51 

52 

51.80 

4.53 

1.78 

4.76 

1.76 

4.98 

51.74 

5.21 

52 

53 

52.80 

4.62 

2.78 

4.85 

2.76 

5.08 

52.73 

5.31 

53 

54 

53.79 

4.71 

3.77 

4.94 

3.75 

5.18 

53.73 

5.41 

54 

55 

54.79 

4.79 

54.77 

5.03 

54.75 

5.27 

54.72 

5.51 

55 

56 

55.79 

4.88 

5.77 

5.12 

55.74 

5.37 

55.72 

5.61 

56 

57 

56.78 

4.97 

6.76 

5.22 

56.74 

5.46 

56.71 

5.71 

57 

58 

57.78 

5.06 

7.76 

5.31 

57.73 

5.56 

57.71 

5.81 

58 

59 

58.78 

5.14 

8.75 

5.40 

58.73 

5.65 

58.70 

5,91 

59 

60 

59.77 

5.23 

9.75 

5.49 

59.72 

5.75 

59.70 

6.01 

60 

61 

60.77 

5.32 

60.74 

5.58 

60.72 

5.85 

60.69 

6.11 

61 

62 

61.76 

5.40 

61.74 

5.67 

61.71 

5.94 

61.69 

6.21 

62 

63 

62.76 

5.49 

62.74 

5.76 

62.71 

6.04! 

62.68 

6.31 

63 

64 

63.76 

5.58 

63.73 

5.86 

63.71 

6.13 

63.68 

6.41 

64 

65 

64.75 

5.67 

64.73 

5.95 

64.70 

6.23 

64.67 

6.51 

65 

6665.75 

5.75 

65.72 

6.04 

65.70 

6.33 

65.67 

6.61 

66 

67 

66.75 

5.84 

66.72 

6.13 

66.69 

6.42' 

66.66 

6.71 

67 

68 

67.74 

5.93 

67.71 

6.22 

67.69 

6.52 

67.66 

6.81 

68 

69 

68.74 

6.01 

68.71 

6.31 

68.68 

6.61 

68.65 

6.91 

69 

70 

69.73 

6.10 

69.71 

6.41 

69.68 

6.71 

69.65 

7.01 

70 

71 

70.73 

6.19 

70.70 

6.50 

70.6-i 

6.81 

70.64]  7.11 

71 

72 

71.73 

6.28 

71.70 

6.59 

71.67 

6.90 

71.64|  7.21 

72 

73 

72.72 

6.36 

72.69 

6.68 

72.66 

7.00 

72.63 

7.31 

73 

74 

73.72 

6.45 

73.69 

6.77 

73.66 

7.09 

73.63 

7.41 

74 

75 

74.71 

6.54 

74.69 

6.86 

74.65 

7.19 

74.62 

7.51 

75 

76 

75.71 

6.62 

75.68 

6.95 

75.65 

7.28 

75.62 

7.61 

76 

77 

76.71 

6.71 

76.68 

7.05 

76.65 

7.38 

76.61 

7.71 

7' 

78 

77.70 

6.80 

77.67 

7.14 

77.64 

7.48 

77.61 

7.81 

7£ 

•79 

78.70 

6.89 

78.67 

7.23 

78.64 

7.57 

78.60 

7.91 

79 

80 

79.70 

6.97 

79.66 

7.32 

79.63 

7.67 

79.60 

8.02 

80 

81 

80.69 

7.06 

80.66 

7.41 

80.63 

7.76 

80.59 

8.12 

81 

82 

81.69 

7.15 

81.66 

7.50 

81.62 

7.86 

81.59 

8.22 

82 

83 

82.68 

7.2i 

82.65 

7.59 

82.62 

7.96 

82.58 

8.32 

83 

84 

83.68 

7'.32 

83.65 

7.69 

83.61 

8.05 

83.58 

8.42 

84 

85 

84.68 

7.41 

84.64 

7.78 

84.61 

8.15 

84.57 

8.52 

85 

86 

85.67 

7.50 

85.64 

7.87 

85.60 

8.24 

85.57 

8.62 

86 

87 

86.67 

7.58 

86.64 

7.96 

86.60 

8.34 

86.56 

8.72 

87 

88 

87.67 

7.67 

87.63 

8.05 

87.59 

8.43 

87.56 

8.82 

88 

89 

88.66 

7.76 

88.63 

8.14 

88.59 

8.53 

88.55 

8.92 

89 

90 

89.66 

7.84 

89.62 

8.24 

89.  5S 

8.63 

89.55 

9.02 

90 

91 

90.65 

7.93 

90.62 

8.33 

90.58 

8.72 

90.54   9.12 

91 

92 

91.65 

8.02 

91.61 

8.42 

91.58 

8.82 

91.54 

9.22 

92 

93 

92.65 

8.11 

92.61 

8.51 

92.5- 

8.91 

92.53 

9.32 

93 

94 

93.64 

8.19 

93.61 

8.60 

93.5- 

9.01 

93.53 

9.42 

94 

95 

94.64 

8.28 

94.60 

8.69 

94.56 

9.11 

94.52 

9.52 

95 

96 

95.63 

8.37 

95.60 

8.78 

95.55 

9.20 

95.52 

9.62 

96 

97 

96.63 

8.4o 

96.59 

8.88 

96.  5o 

9.30 

96.51 

9.72 

97 

98 

97.63 

8.54 

97.59 

8.9- 

97.5o 

9.39 

97.51 

9.82 

98 

99 

98.62 

8.63 

98.59 

9.06 

98.54 

9.49 

98.50 

9.92 

99 

10 

99.6-2 

8.72 

99.58 

9.1- 

99.54 

9.58 

99.50  10.02 

100 

«J 

CO 

Dep. 

Lat 

Dep 

Lat 

Dep 

Lat. 

Dep.|  Lat. 

to 

3 

85  Deg 

34  1  Deg 

84iDeg, 

84}  Deg. 

5 

12 

50 


TRAVERSE  TABLE. 


5 

6  Deg. 

6[  Deg. 

6^  Deg. 

6|  Deg. 

g 

r*" 

Lat. 

Dep. 

Lat.iDep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

i 

0.99 

0.10 

0.99J  0.11'i  0.99 

0.11 

0.99 

0.12 

i 

2 

1.99 

0.21 

1.99 

0.221    1.99 

0.23 

1.99 

0.24 

2 

3 

2.98 

0.31 

2.98 

0.33    2.98 

0.34 

2.98 

0.35 

3 

4 

3.98 

0.41 

3.981  0.44 

1  3.97 

0.45 

3.97 

0.47 

4 

5 

4.97 

0.52 

4.97i  0.54 

4.97 

0.57 

4.97 

0.59 

5 

6 

5.97 

0.63 

5.96 

0.65 

5.96 

0.68 

5.96 

0.71 

6 

7 

6.96 

0.73 

6.96;  0.76 

6.96 

0.79 

6.95 

0.82 

7 

8 

7.96 

0.84 

7.95J  0.87 

7.95 

0.91 

7.94 

0.94 

8 

9 

8.95 

0.94 

8.95[  0.98 

8.94 

1.02 

8.94 

1.06 

9 

10 

9.95 

1.05 

9.94 

1.09 

9.94 

1.13 

9.93 

1.18 

10 

11 

10.94 

.15 

10.93 

1.20 

10.93 

1.25 

10.92 

1.29 

11 

12 

11.93 

.25 

11.93    1.31 

11.92 

1.36 

11.92 

1.41 

12 

13 

12.93 

.36 

12.92 

1.42 

12.92 

1.47 

12.91 

1.53 

13 

14 

13.92 

.46 

13.92 

1.52 

13.91 

1.59 

13.90 

1.65 

14 

15 

14.92 

.57 

14.91 

1.63 

,14.90 

1.70 

14.90 

1.76 

15 

16 

15.91 

.67 

15.90 

1.74 

115.90 

1.81 

15.89 

1.88 

16 

17 

16.91 

.78 

16.90 

1.85 

|16.89 

1.92 

16.88 

2.00 

17 

18 

17.90 

.88 

17.89 

1.96 

117.88 

2.04 

17.88 

2.12 

18 

19 

18.90 

.99 

18.89 

2.07 

i  18.88 

2.15 

18.87 

2  23 

19 

20 

19.89 

2.09 

19.88 

2.18)19.87 

,2.26 

19.86 

2.35 

20 

t 

21 

20.88 

2.20 

20.88   2.29  !la0.87 

2.38 

20.85 

2.47 

21 

2221.88 

2.30 

21.87i  2.40  |21.86 

2.49 

21.85 

2.59 

22 

2322.87 

2.40 

22.86 

2.50'  22.86 

2.60 

22.84 

2.70 

23 

24 

23.87 

2.51 

23.86 

2.61;  123.85 

2.72 

23.83 

2.82 

2/j 

25 

24.86 

2.61  24.85,  2.72'  |24.84 

2.83 

24.83 

2.94 

25 

26 

25.86 

2.72!!25.85 

2.83'!25.83 

2.94 

25.82 

3.06 

26 

27 

26.85 

2.82 

26.84 

2.94  26.83 

3-06 

26.81 

3.17 

27 

28 

27.85 

2.93 

27.83 

3.05  i27.82 

3.17 

27.81 

3.29 

28 

29 

28.84 

3.03 

28.83 

3.16  28.81 

3.28 

28.80 

3.41 

29 

30 

29.84 

3.14 

29.82 

3.27 

,29.81 

3.40 

29.79 

3.53 

30 

31 

30.83 

3.24 

30.82i  3.37  p30.80 

3.51 

30.79 

3.64 

31 

32  31.82 

3.34 

31.81 

3.48:;31.79 

3.62 

31.78 

3.76 

32 

3332.82 

3.45 

32.80 

3.59  '32.79 

3.74 

32.77 

3.88 

33 

3433.81 
3534.81 

3.55  33.80 
3.66  34.79 

3.70  33.781  3.85 
3.81  :34.78   3.96 

33.76 
34.76 

4.00 
4.11 

34 

35 

3635.80 

3.76 

35.79 

3.92  '35.77 

4.08 

35.75 

4.23 

36 

37 

36.80 

3.87 

36.78 

!  4.03  ;36.76 

4.19 

36.75 

4.35 

37 

38 

37.79 

3.97 

37.77 

'  4.  1  i1  37.76 

4.30 

37.74 

4.47 

38 

39 
40 

38.79 
39.78 

4.08 
4.18 

38.77J  4.25i!38.75    4.41 
39.76i  4.35  39.74   4.53 

38.73 
39.72 

4.58 
4.70 

39 

40 

41 

40.78 

4.29J  40.76   4.46!  40.74   4.64 

40.72 

4.82 

41 

42 

41.77 

4.39  41.75  4.57  41.73 

4.76 

41.71 

4.94 

43 

43 

42.76 

4.49 

42.74:  4.68  42.72 

4.87 

42.70 

5.05 

43 

44 

43.76 

4.60  43.74   4.79  43.72 

4.98 

43.70 

5.17 

4-1 

45 

44.75 

4.70  44.73   4.90  ;44.71 

5.09 

44.69 

5.29 

45 

46 

45.75 

4.81 

45.73   5.01  45.70 

5.21 

45.68 

5.41 

46 

47 

46.74 

4.91 

46.  72  '5.  12  46.70 

5.32 

46.67 

5.52 

41 

48 

47.74 

5.02 

47.71 

5.23 

;47.69 

5.43 

47.67 

5.64 

48 

49 

48.73 

5.12 

48.71 

i  5.34 

48.69 

5.55 

48.66 

6.76 

49 

50 

49.73 

5.23 

49.70J  5.44 

49.68 

5.66 

49.66 

5.88 

50 

Lat. 

iDep. 

Dep. 

oa 

Dep. 

Lat. 

I  Lat. 

Dep. 

Lat. 

ts 

S 

84  Deg. 

|83|Deg. 

|83£Deg. 

83iDeg. 

I 

TRAVERSE  TABLE. 


b 

6  Deg. 

6|  Deg. 

6  £  Deg. 

G^Deg. 

9 

s. 

Lat. 

)ep. 

Lat.  i  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

CO 
«•»• 

51 

0.72 

5.33 

50.701 

5.55 

0.67 

5.77 

50.65 

5.99 

51 

52 

1.72 

5.44 

51.69! 

5.66 

1.67 

5.89 

1.64 

6.11 

52 

53 

2.71 

5.54 

52.68 

5.77 

2.66 

6.00 

52.63 

6.23 

53 

54 

3.70 

5.64 

53.68 

5.88 

3.65 

6.11 

53.63 

6.35J  54 

55 

4.70 

5.75 

54.67 

5.99 

54.65 

6.23 

54.62 

6.46 

55 

56 

5.69 

5.85 

55.67 

•6.10 

65.64 

6.34 

55.61 

6.58|  56 

57 

6.69 

5.96 

56.66 

6.21 

56.63 

6.45 

56.60 

6.70 

i  57 

58 

7.68 

6.06 

57.66 

6.31 

57.63 

6.57 

57.60 

6.82 

58 

59 

8.68 

6.17 

58.65: 

6.42 

58.62 

6.68 

58.59 

6.93   59 

60 

9.67 

6.27 

59.64| 

6.53 

59.61 

6.79 

59.58 

7.05   60 

61 

0.67 

6.38 

60.64 

6.64 

60.61 

6.91 

60.58 

7.17   61 

62 

1.66 

6.48 

61.63 

6.75 

61.60 

7.02 

61.57 

7.29   62 

63 

2.65 

6.59 

62.63 

6.86 

62.60 

7.13 

62.56 

7.40   63 

64 

3.65 

6.69 

63.62 

6.97 

63.59 

7.25 

63.56 

7.52   64 

65 

4.64 

6.79 

64.61 

7.08 

64.58 

7.36 

64.55 

7.64   65 

66 

5.64 

6.90 

65.61 

7.19 

65.58 

7.47 

65.54 

7.76   66 

67 

6.63 

7.00 

66.60; 

7.29 

66.57 

7.58 

66.54 

7.8? 

67 

68 

7.63 

7.11  67.60 

7.40 

67.56 

7.70 

67.53 

7.99   68 

69 

8.62 

7.21 

68.59 

7.51 

68.56 

7.81 

68.52 

8.11    69 

70 

9.62 

7.32 

69.58) 

7.62 

69.55 

7.92 

69.51 

8.23,  70 

71 

0.61 

7.42 

70.58 

7.73 

70.54 

8.04 

70.51 

8.351  71 

72 

1.61 

7.53 

71.57 

7.84 

71.54 

8.15 

71.50 

8.4f 

;  72 

73 

2.60 

7.63 

72.57 

7.95 

72.53 

8.26 

72.49 

8.58   73 

74 

3.59 

7.74  73.56 

8.06 

73.52 

8.38 

73.49 

8.70   74 

75 

4.59 

7.84174.55 

8.17 

74.52 

8.49 

74.48 

8.8$ 

»   75 

76 

5.58 

7.94 

75.55 

U27 

75.5 

8.60 

75.47 

8.93   76 

77 

6.58 

8.05 

76.54 

8.38 

76.5 

8.7 

76.47 

9.05   77 

78 

7.57 

6.15 

77.54 

8.49 

77.50 

8.8 

77.46 

9.17   78 

79 

8.57 

8.26 

78.53 

8.60 

78.4 

8.9 

78.45 

9.29   79 

80 

9.56 

8.36 

79.53J  8.71 

79.4 

9.0 

79.45 

9.4< 

)   80 

81 

80.56 

8.47 

90.62 

8.82 

80.4 

9.1 

80.4 

9.52    81 

82 

81.55 

8.57 

81.51 

8.9.' 

81.4 

9.2 

81.43 

9,64   82 

83 

82.55 

8.68 

82.51 

9.04 

82.4 

9.4 

82.42 

9.76   83 

84 

83.54 

8.78 

83.50 

9.14 

83.4 

9.5 

83.4 

9.87    84 

85 

84.53 

8.88 

84.50 

9.25 

84.4 

9.6 

84.4 

9.99   85 

86 

85.53 

8.99 

85.49 

9.36 

85.4 

9.7 

85.4 

10.11   86 

87 

86.52 

9.09 

86.48 

9.4 

86.44 

9.8 

86.4 

10.23   87 

88 

87.52 

9.201  87.48 

9.58 

87.4S 

9.9 

87.3 

10.34   88 

89 

88.51 

9.30 

88.47 

9.6S 

88.49 

10.0 

88.3 

10.46   89 

90 

89.51 

9.41  89.47 

9.80 

89.4 

10.1 

89.3 

10.58   90 

91 

90.50 

9.51  90.46J  9.9 

90.4 

10.3 

90.3 

10.70  91 

92 

91.50 

9.62i  91.4510.0 

91.4 

10.4 

91.3 

10.81   92 

93 

92.49 

9.72 

92.45 

10.1 

92.4 

10.5 

92.3 

1C.93   93 

94 

93.49 

9.83 

93.44:10.2 

93.4 

10.6 

93.3 

11.05   94 

95 

94.48 

9.93 

94.4410.3 

94.3 

10.7 

94.3 

11.17   95 

96 

95.4 

10.03 

[95.4310.4 

95.3 

10.8 

95.3 

11.28   96 

97 

96.4 

10.14 

!  96.42  10.5 

96.3 

10.9 

96.3 

11.40   97 

9 

97.4 

10.24 

!  97.42  10.6 

97.3 

11.0 

97.3 

11.52  98 

99 

98.4 

10.35ll98.41 

10.7 

98.3 

11.2 

9ft3 

11.64   99 

100 

99.4. 

10.45 

99.41 

10.8 

99.3 

11.3 

99.3 

11.75100 

| 

Dep 

Lat. 

fc 

Lat 

Dep 

Lat 

Dep 

Lat 

'"« 

84  Deg. 

|s34Deg 

83iDeg 

83,Deg 

"5 

TRAVERSE  TABLE. 


g 

55* 

7Deg. 

7J  Deg. 

7J  Deg. 

7JJ 

. 

Lat. 

Jeg. 

Dep. 

£ 

Lat. 

Dep. 

Lat.  Dep. 

Lat. 

Dep. 

l 

0.99 

0.12 

0.99   0.13 

0.99 

iO.13 

0.99 

0.13 

i 

2 

1.99 

0.24 

1.98 

0.25 

1.98 

0.26 

1.98 

0.27 

2 

2 

2.98 

0.37 

2.98 

0.38    2.97 

0.39 

2.97 

0.40 

3 

4 

3.97 

0.49 

3.97 

0.50    3.97)  0.52 

3.9& 

0.54 

4 

5 

4.96 

0.61 

4.96 

0.63    4.96 

0.65 

4.95 

0.67 

e 

6 

5.96 

0.73 

5.95 

0.76 

5.95 

0,78 

5.95   0.81 

6 

7 

6.95 

0.85 

6.94 

0.88 

6.94 

0.91 

6.94 

0.94 

8 

7.94 

0.97 

7.94 

1.01 

7.93 

1.04 

7.93)     .08 

8 

9 

8.93 

1.10 

8.93 

1.14 

8.92 

1.17 

8.92 

.21 

9 

10 

9.93 

1.22 

9.92 

1.26 

9.91 

1.31 

9.91 

.35 

10 

11 

10.92 

1.34 

10.91 

1.39 

10.91 

.44 

10.90 

.48 

11 

12 

11.91 

1.46 

11.90 

1.51  1  11.90 

.57 

11.89 

.62 

12 

13 

12.90 

1.58 

12.90 

1.6412.89     .70 

12.88 

.75 

13 

14 

13.90 

1.71 

13.89 

1.77113.88 

.83 

13.87 

1.89 

14 

15 

14.89 

1.83 

14.88 

1.89)14.87 

.96 

14.86 

2.02 

15 

16 

15.88 

1.95 

15.87 

2.02  I15.86J  2.09 

15.85 

2.16 

16 

17 

16.87 

2.07 

16.86 

2.15*16.85 

2.22 

16.84 

2.29 

17 

18 

17.87 

2.19 

17.86 

2.271  117.85 

2.35 

17.84 

2.43 

18 

19 

18.86 

2.32 

18.85 

2.40 

18.84 

2.48 

18.83 

2.56!  19 

20 

19.85 

2.44 

19.84 

2.52 

19.83 

2.61 

19.82 

2.70   20 

21 

20.84 

2.56 

20.83 

2.65 

20.82 

2.74 

20.81 

2.831  21 

22 

21.84 

2.68 

21.82 

2.78 

21.81 

2.87 

21.80 

2.97 

22 

23 

22.83 

2.80 

22,82 

2.90 

22.80 

3.00 

22.79 

3.10   23 

24 

23.82 

2.92 

23.81 

3.03 

23.79;  3.13 

23.78 

3.24!  24 

25 

24.81 

3.05 

24.80 

3.15 

24.79 

3.26 

24.77:  3,37    25 

26 

25.81 

3.17 

25.79 

3.28 

25^78 

3.39 

25.76 

3.51   26 

27 

26.80 

3.29 

26.78 

3.41!  ,26.77   3.52 

26.75 

3.641  27 

28 

27.79 

3.41 

27.78 

3.53 

27.76 

3.65 

27.74 

3.78i  28 

29 

28.78 

3.53 

28.77 

3.66 

28.75 

3.79 

28.74 

3.91 

29 

30 

29.78 

3.66 

29.76 

3.79 

29.74 

3.92 

29.73 

4.05 

30 

31 

30.77 

3.78 

30.75 

3.91 

30.  7S  4.05 

30.72 

4.18   31 

32 

31.76 

3.90 

31.74 

4.04 

31.73 

4.18 

31.71 

4.32 

32 

33 

32.75 

4.02 

32.74 

4.16 

32.72 

4.31 

32.70 

4.45 

33 

34 

33.75 

4.14 

33.73 

4.29 

33.71 

4.44 

33.69 

4.58   34 

35 

34.74 

4.27 

34.72 

4.42 

34.70!  4.57 

34.68 

4.72 

35 

36 

35.73 

4.39 

35.71 

4.54 

35.691  4.70 

35.67 

4.85J  36 

37 

36.72 

4.51 

36.70 

4.67 

36.68 

4.83 

36.66 

4.99 

•37 

38 

37.72 

4.63 

37.70 

4.80 

37.67 

4.96 

37.65 

5.12 

38 

39 

38.71 

4.75 

38.69 

4.92 

38.67 

5.09 

38.64 

5.26 

39 

40 

39.70 

4.87 

39.68 

5.05 

39.66 

5.22 

39.63   5.39 

40 



. 



41 

40.70 

5.00 

40.67 

5.17 

40.65   5.35 

40.63 

5.53 

41 

42 

41.69 

5.12 

41.66 

5.30 

41.64 

5.48 

41.62 

5.66 

42 

43 

42.68 

5.24 

42.66 

5.43 

42.63 

5.61 

42.61 

5.80 

43 

44 

43.67 

5.36 

43.65 

5.55 

43.62 

5.74 

43.60 

5.93 

44 

45 

44.67 

5.48 

44.64 

5.68 

44.62 

5.87 

44.59 

6.07 

45 

46 

45.66 

5.61 

45.63 

5.81 

45.61 

6.00 

45.58 

6.20 

46 

47 

46.65 

5.73 

46.62 

5.93 

46.60   6.13 

46.57 

6.34;  47 

48 

47.64 

5.85 

47.62 

6.06 

47.59]  6.27 

47.56 

6.47 

48 

49 

48.63 

5.97 

48.61 

6.18 

48.58 

6.40 

48.55 

6.61 

49 

50 

49.63 

6.09 

49.60 

6.31 

49.57 

6.53 

49.54 

6.74 

50 

•s 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 



Dep. 

Lat. 

tJ 

S 

83  Deg. 

82}Deg. 

82iDeg.  82iDeg. 

S 

TRAVERSE  TABLE. 


£  7  Deg.     7;  Deg. 

71  Deg. 

11  Deg.  g 

r   Lat. 

Dep.    Lat. 

Dep. 

Lat.  |  Dep. 

Lat.  Dep.  r 

51!50.62 

6.22  50.59 

6.44 

50.56;  6.66 

50.53  8.881  51 

5251.61 

6.34  51.58   6.56!  51.56   6.79 

51.53   7.01    52 

5352.60 

6.46,52.58!  6.69  |52.55   6.92 

52.52   7.16!  53 

5453.60 

6.58  53.57    6.81  53.54   7.05: 

53.51    7.28'  54 

5554.59 

6.70  54.56 

6.94  54.53   7.18; 

54.50   7.42s  55 

5655.58 

6.82  55.55 

7.07 

55.52   7.31! 

55.49    7.55:  56 

57  56.58 

6.95;  56.54 

7.19 

56.51    7.44'56.48i  7.69!  57 

58  57.57 

7.07  57.54 

7.32 

57.50   7.57 

57.47    7.82,  58 

5958.56 

7.19  58.53 

7.45 

58.50   7.70 

58.46    7.96   59 

6059.55 

7.31  159.52 

7.57 

59.49   7.83 

59.45   8.09;  60 

61  60.55 

7.43  60.51 

7.70 

60.48    7.96 

60.44!  8.23    61 

6261.54 

7.56  61.50 

7.82i61.47    8.09  161.43   8.36   62 

63  62.53 

7.68  62.50 

7.95  62.46    8.22  62.42   8.50   63 

6463.52 

7.80  '63.49 

8.08  63.45   8.35  63.42   8.63!  64 

65  64.52 

7.92  64.48 

8.20164.44   8.48!64.41    8.77J  65 

6665.51 

8.04  65.47 

8.33  65.44   8.61  65.40   8.90   66 

67  66.50 

8.  17^66.46 

8.46  166.43;  8.75  66.39   9.04   67 

6867.49 

8.29  67.46    8.58  67.42!  8.88  67.38   9.17   68 

69  68.49 

8.41  68.45 

8.71 

68.41!  9.01  68.37   9.30   69 

70  69.48 

8.53  69.44 

8.83 

;69.40'  9.14i  69.36|  9.44   70 

71  70.47 

8.65  70.43 

8.96 

70.391  9.27!<70.35   9.57^  71 

7271.46 

8.77  71.42 

9.09 

71.38   9.40h71.34   9.71    72 

73  72.46 

8.90  72.42 

9.21 

72.38!  9.53i  72.33   9.84   73 

74  73.45 

9.02  73.41 

9.34  73.37   9.66!!73.32   9.98    74 

75  74.44 

9.14  74.40 

9.46i74.36    9.79iJ74.31  10.11    75 

76  75.43 

9.26  75.39 

9.59J75.35   9.92|  75.31  10.25    76 

77  76.43 

9.38  76.38 

9.72i  76.34  10.05  76.30  10.38    77 

78  77.42 

9.51  77.38 

9.84:77.3310.18 

77.2910.52    78 

79  78.41 

9.63  78.37 

9.97  78.3210.31 

78.2810.65    79 

80  79.40 

9.75  79.3610.10  79.3210.44 

79.27  '10.  79    80 

81  80.40   9.87'  80.35J10.22 

80.31  10.57 

80.26  10.92   81 

82  81.39!  9.99  81.34  10.35;  81.30  10.70 

81.2511.06   82 

8382.38  10.12  82.34  10.47  82.29  10.83 

82.2411.19    83 

8483.37  10.24  83.331  10.60;  83.28  10.96 

83.2311.33   84 

85  84.37  10.36  ;  84.32 

10.73  84.27  11.09 

84.2211.46   85 

8685.36i  10.48  '85.31 

10.86  85.2611.23185.2111.60   86 

8786.3510.60  86.  30)10.98  86.26  Il.36ii86.2111.  73   87 

8887.3410.72  ;87.30  1  1.11  87.25  11.49  i87.20  11.87   88 

89,88.3410.85  88.291  11.231  88.24  11.621  88.19  12.00.  89 

90,89.33  10.97  189.28 

11.36  89.2311.75  89.1812.14;  90 

91  90.32,  11.  09  90.27 

11.48'  90.22  11.88  90.17  12.27   91 

9291.31  11.21  '91.26 

11.61  91.21  12.01!  91.  16J12.41   92 

9392.31  11.33  92.26 

11.7492.2012.1492.1512.54   93 

9493.3011.46  93.25 
9594.2911.58  94.24 

11.86  J93.20  12.27i  93.  14  12.68   94 
11.99  S94.19  12.40:  94.13  12.81    95 

9695.2811.70  95.23:12.12  95.18  12.53  95.12  12.95   96| 

9796.2811.82  96.22 

12.2496.1712.6696.1113.08   97 

9897.2711.94  97.22 

12.37  97.16  12.79  ,97.10113.22   98 

99  98.26i  12.07:98.21 
10099.2512.19J99.20 

12.49,  98.15  12.921  98.10  13.35    99 
12.62;  |99.  14  13.051  99.09  13.49  100 

•          1           ___ 

1  1 

l          

+1   Dep.  I  Lat.  Dep. 

Lat. 

Dep.   Lat. 

Dep.  Lat.  +j> 

S  j  83Deg.  82'Deg.  82peg.  82'Deg.S 

TRAVERSE  TABLE. 


g  8  Deg. 

8£  Deg.jjSi  Deg. 

8f  Deg. 

0 

f*   Lat.lDep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

1    0.99:  0.14 

0.99 

0.14 

0.99 

0.15 

0.99 

0.15 

2    1.98!  0.28 

1.98 

0.29 

1.98 

0.30 

1.98 

0.30 

c 

3   2.971  0.42 

2.97 

0.43 

2.97 

0.44 

2.97 

0.46 

J 

4   3.96,  0.56 

3.96 

0.57 

3.96 

0.59 

3.95 

0.61 

/ 

5   4.95!  0.70 

4.95 

0.72! 

4.95 

0.74 

4.94 

0.76 

i 

6   5.94   0.84 

5.94 

0.86 

5.93 

0.89JI  5.93 

0.91 

1 

7   6.93!  0.97 

6.93 

l.OOi 

6.92 

1.03!!  6.92 

1.06 

' 

8    7.92|  1.11 

7.92 

.15 

7.91 

1.18    7.91 

1.22 

1 

9   8.9ll  1.25 

8:91 

.29 

8.90 

1.33  1  8.90 

.37 

! 

HT9.90J  1.39 

9.90 

.43 

9.89 

1.48    9.88 

.52 

10 

1—  —  , 

__;  

- 



1110.89    1.53  10.89 

.58 

10.88 

1.63 

10.87 

.67 

I2<11.88    1.67)11.88 

.72: 

11.87 

1.77 

11.86 

.83 

c 

13:12.87!  1.81,12.87 

.87,112.86 

1.92  12.85 

.98 

i 

1413.86    1.95  13.86 

2.01 

13.85   2.07  13,84 

2.13 

i 

1514.85;  2.09'l4.-85 

2.15)14.84!  2.22  14.83!  2.28 

5 

16  15.84!  2.23 

15.84 

2.30  J15.82I  2.36  15.81 

2.43 

16 

17  16.83'  2.37  16.83 

2.44J 

16.81   2.51:16.80 

2.59 

17 

1817.82!  2.51  17.81 

2.58! 

17.80   2.66!  17.79 

2.74 

18 

19  18.82!  2.64 

18.80 

2.73 

18.79 

2.81 

18.78 

2.89 

19 

2019.81    2.78 

19.79 

'2.87 

19.78 

2.96  19.77 

3.04 

20 

2120.80!  2.92 

20.78 

3.01 

20.77 

3.10  20.76 

3.19 

21 

2221.79!  3.06 

21.77 

3.16! 

21.76 

3.25 

21.74 

3.35 

22 

2322.78!  3.20 

22.76 

3.30|!22.75 

3.40 

22.73 

3.50 

23 

2423.77!  3.34  23.75 

3.44!  '23.74   3.55 

23.72 

3.65 

24 

2524.76   3.48!  24.74!  3.59 

24.73   3.70 

24.71 

3.80 

25 

2625.75   3.62J  25.73'  3.73, 

25.71    3.84 

25.70 

3.96 

26 

2726.74   3.76  26.72   3.87  26.70   3.99 

26.69 

4.11 

27 

2827.73   3.90127.71 

4.02: 

27.69 

4.14 

27.67 

4.26 

28 

2928.72    4.04J28.70I  4.16i 

28.68 

4.29 

28.66 

4.41 

29 

3029.71    4.18;29.69]  4.30; 

29.671  4.43 

29.65 

4.56 

30 

3130.70   4.3'li  30.68!  4.45 

30.66   4.58 

30.641  4.  "2 

31 

3231.69    4.45  31.67   4.59 

31.65   4.73 

31.63   4.87 

32 

3332.68   4.5932.66 

4.74 

32.64   4.88! 

32.62!  5.02 

33 

34  33.67   4.73  33.65 

4.88 

33.6§   6.0333.60   5.17 

34 

3534.66   4.87'  34.64 

5.02 

34.62;  6.17  34.59    5.321  35 

3635.65   5.01  35.63 

5.17 

35.60i  5.32  '35.58    5.481  36 

3736.64   5.1536.62 

5.31 

36.59   5.47  36.57!  5.63 

37 

3837.63    5.29  37.61 

5.45 

37.58'  5.62  '37.561  5.78 

38 

3938.62   5.4338.60 

5.60 

38.57!  5.76138.55:  5.93    39 

4039.61,  5.57;  39.59 

5.74 

39.56;  5.91  ;  39.53!  6.08   40 

i  J1  ;_ 

' 

1  1  

4140.60   5.71  40.58 

5.88 

40.55    6.06 

40.52   6.24   41 

4241.59    6.85  41.57 

6.03 

41.54   6.21 

41.51    6.39   42 

4342.58    5.98  42.56 

6.17 

42.53    6.36 

42.50   6.54   43 

4443.57    6.12  43.54 

6.31 

43.52!  6.50 

43.49    6.69   44 

4544.56    6.26  44.53 

6.46 

44.5l|  6.65  44.48   6.85   45 

4645.55    6.40  45.52 

6.60 

45.49|  6.80  !45.46    7.00  46 

47  46.54    6.54  46.51 

6.74 

46.481  6.95  46.45   7.15J  47 

4847.53    6.68  47.50 

6.89 

47.47:  7.09  47.44    7.30   48 

49:48.52:  6.82  48.49 

7.03 

48.46   7.24:48.43    7.45  49 

50,49.51    6.96  49.48 

7.17 

49.45;  7.39 

49.42    7.61    50 

^j  Dep.    Lat.  Dep. 

Eft 

Lat. 

Dep.  Lat. 

Dep.  Lat.  ^J 

5    82  Deg.  81  f  Deg.  81^Deg. 

SliDeg.  Q 

TRAVERSE  TABLE. 


0!  8  Deg. 

81  Deg. 

81  Deg. 

8|  Deg. 

0 

?*"  Lat.  Dep. 
5150.50!  7.10 

Lat.  |Dep.! 

60.47    7.32 

Lat.  i  Dep. 
50.44    7.54 

Lat. 

50.41 

Dep. 
7.76 

a 

51 

5251.49    7.24,51.46    7.4651.43 

7.69 

51.39 

7.91   52 

53  52.48 

7.38  152.45    7.61  52.42 

7.83 

52.38 

8.06   53 

54  53.47 

7.52 

53.44|  7.75  53.41 

7.98)53.37 

8.21    54 

55  54.46 

7.65 

64.431  7.89:54.40 

8.  IS;  64.36 

8.37   55 

56  55.46 

7.79 

55.42 

8.04 

55.38 

8.28;  55.35 

8.52   56 

57  56.45 

7.93 

56.41 

8.18 

56.37 

8.43  166.34 

8.67   67 

5857.44 

8.07 

57.40 

8.32 

57.36 

8.57, 

57.32 

8.82   58 

5958.43 

8.21 

58.39 

8.47 

58.35 

8.72 

58.31 

8.98   59 

6059.42 

8.35  59.38 

8.61 

59.34 

8.87 

59.30 

9.13   60 

616CU1 

8.49  60.37 

8.75  60.33 

9.02J60.29 

9.28 

61 

62,61.40 

8.63  61.36 

8.90J  !61.32 

9.16  161.28 

9.43 

62 

63  62.39 

8.77  62.35 

9.04|  62.31 

9.31  162.27 

9.58   63 

6463.38 

8.91  63.34 

9.18 

63.30 

9.46163.26 

9.74i  64 

65  64.37 

9.05  64.33 

9.33 

64.29 

9.61  164.24 

9.89   65 

66  65.36 
67  66.35 

9.19 
9.32 

65.32 
66.31 

9.47 
9.61 

65.28 
66.26 

9.76  65.23 
9.90  66.22 

10.04   66 
10.19   67 

68;67.34 

9.46 

67.30 

9.76 

67.25 

10.05 

67.21 

10.34   68 

69  68.33 

9.60  68.29 

9.  90i  |68.24 

10.20 

68.20 

10.50 

69 

70  69.32 

9.74  69.28 

10.04  69.23 

10.35 

69.19 

10.65 

70 

71!70.31 

9.88  70.27 

10.19'  70.22 

10.49 

70.17 

10.80 

71 

7271.30 
73j  72.29 
7473.28 

10.02i  71.25 
10.  161  72.24 
10.30;  73.23 

10.33 
10.47 
10.62 

71.21 

72.20 
73.19 

10.64  71.16 
10.79  72.15 
10.94  73.14 

10.95 
11.10 
11.26 

72 
73 
74 

75  74.27 

10.44  74.22 

10.76 

74.18 

11.09 

74.13 

11.41 

75 

76 

75.26 

10.58  75.21 

10.91 

75.J7 

11.23 

75.12 

11.56 

76 

77 

76.25  10.  72[  76.20 

11.05 

76.15 

11.38 

76.10 

11.71 

77 

78 
79 

77.24  10.86ji77.19 
78.23  10.99  78.18 

11.19 
11.34 

77.14 
78.13 

11.53 
11.68 

77.09 
78.08 

11.87 
12.02 

78 
79 

80 

79.22 

11.13 

79.17 

11.48 

79.12 

11.82 

79.07 

12.17 

80 

81  80.21 
8281.20 

11.27i;80.16 
11.41  h81.  15 

11.62 
11.77 

80.11 
81.10 

11.97  80.06 
12.12181.05 

12.32 
12.47 

81 

82 

8382.19 

11.55  82.14 

11.91 

82.09 

12.27 

82.03 

12.63   83 

8483.18 

11.69  ;83.13 

12.05  83.08 

12.42 

83.02 

12.78   84 

8584.17 

11.83  84.12 

12.20;  84.07 

12.56 

84.01 

12.93   85 

8685.16 

11.97:85.11 

12.34 

85.06 

12.71 

85.00 

13.08   86 

8786.15 

12.11  86.10 

12.48 

86.04 

12.86 

85.99 

13.23   87 

8887.14 

12.25  J87.09 

12.63  87.03 

13.01 

86.98 

13.39    88 

89 

88.13 

12.39!  88.08 

12.77j88.02 

13.16 

87.96 

13.54   89 

90 

89.12 

12.53 

89.07 

12.91 

89,01 

13.30 

88.95 

13.69,  90 

91 

92 

90.11 
91.10 

12.66 
12.80 

90.06 
91.05 

13.06  i  90.00 
13.20'  J90.99 

13.45 
13.60 

89.94 
90.93 

13.84'  91 
14.00!  92 

93 

92.09 

12.94  92.04 

13.34!  91.98 

13.75 

91.92 

14.15!  93 

94 

93.09 

13.08  93.03 

13.49  92.97 

13.89! 

92.91 

14.30   94 

95 
96 

94.08 
95.07 

13.22  94.02 
13.36  95.01 

13.63 
13.78 

93.96 
94.95 

14.04; 

14.19! 

93.89 
94.88 

14.45   95 
14.60   96 

97 

98 

96.06 
97.05 

13.50i  96.00 
13.64196.99 

13.92  95.93 
14.06j  96.92 

14.34 
14.49 

95.87 
96.86 

14.76   97 
14.9i:  98 

99 

98.04 

13.78 

97.98 

14.21  97.91 

14.63 

97.85 

15.06    99 

100 

99.03 

13.92 

98.97 

14.35 

98.SO 

14.78IJ98.84 

15.21100 

,g 

Dep. 

Lat. 

Dep. 

Lat. 

,Dep. 

Lat: 

Dep. 

Latj^j 

I  tn 

82  Deg. 

OlfDeg. 

SliDeg. 

;._« 

TRAVERSE  TABLE. 


g  9  Deg. 

9±  Deg. 

9i  Deg. 

9|  Deg, 

o 

f*  Lat.  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p- 

1   0.99J  0.16 

0.99 

0.16 

0.99 

0.17 

i  0.99 

0.17 

1 

2   1.98  0.31 

1.97 

0.32 

1.97 

0.33 

1  1.97 

0.34 

2 

3   2.96 

0.47 

2.96 

0.48 

2.96 

0.50 

i  2.96 

0.51 

3 

4  3.95 

0.63 

3.95 

0.64 

3.95 

0.66 

3.94 

0.68 

4 

5j  4.94 

0.78 

4.93 

0.80 

4.93 

0.83 

4.93 

0.85 

5 

6J  5.93 

0.94 

5.92 

0.96 

5.92 

0.99 

!  5.91 

1.02 

6 

7   6.91 

.10 

6.91 

1.13 

6.90 

.16 

6.90 

1.19 

1 

8!  7.90 

.25 

7.90 

1.29 

7.89 

.32 

7.88 

1.35 

8 

9   8.89 

.41 

8.88 

1.45 

8.88 

.49 

i  8.87 

1.52 

9 

10   9.88 

.56 

9.87 

1.61 

9.86 

.65 

9.86 

1.69 

10 

11  10.86 

.72 

10.86 

1.77 

10.85 

.82 

10.84 

1.86 

11 

1211.85 

.88 

11.84 

1.93 

11.84 

.98 

11.83 

2.03 

12 

13  12.84 

2.03 

12.83 

2.09112.82 

2.15 

12.81 

2.20 

13 

1413.83 

2.19 

13.82 

2.25 

13.81 

2.31 

13.80 

2.37 

14 

15  14.82 

2.35 

14.80 

2.41 

14.79 

2.48 

;14.78 

2.54 

15 

16  15.80 

2.50 

15.79 

2.57 

15.78 

2.64 

15.77 

2.71 

16 

17  16.79 

2.66 

16.78 

2.73 

16.77 

2.81 

16.75 

2.88 

17 

1817.78 

2.82 

17.77 

2.89 

17.75 

2.97 

17.74 

3.05 

18 

1918.77 

2.97 

18.75 

3.05 

18.74 

3.14 

18.73 

3.22 

19 

2019.75 

3.13 

19.74:  3.21 

19.73 

3.30 

19.71 

3.39 

20 

21  '20.74  3.29 

20.73  3.38 

20.71 

3.47 

20.70 

3.561  21 

2221.73   3.44 

21.71 

3.54 

21.70 

3.63 

21.68 

3.731  22 

2322.72  3.60 

22.70 

3.70 

22.68 

3.80 

22.67 

3.90   23 

2423.70  3.75 

23.69 

3.86 

23.67 

3.96 

23.65 

4.06   24 

2524.69   3.91 

24.67 

4.02 

24.66 

4.131  24.64 

4.23   25 

2625.681  4.®7 

25.661  4.18 

25.64 

4.29 

25.62 

4.401,  26 

2726.67   4.22 

26.65   4.34 

26.63 

4.46 

26.61 

4.57 

27 

2827.66   4.38 

27.64 

4.50 

27.62 

4.62 

27.60 

4.74 

28 

2928.64 

4.54 

28.62 

4.66128.60 

4.79 

28.58 

4.91 

2! 

3029.63 

4.69 

29.611  4.82!  29.59 

4.95 

29.57 

5.08   30 

3130.62 

4.85  30.60 

4.98 

30.57 

5.12 

30.55 

5.25   31 

3231.61 

5.01  31.58 

5.14 

31.56 

5.28 

31.54 

5.42   32 

33  32.59 

5.16,32.57!  5.30i  32.55 

5.45 

32.52 

5.59   33 

3433.58 

5.32:33.56 

5.47133.53 

5.61 

33.51 

5.76   34 

3534.57 

5.48!34.54 

5.63134.52 

5.78 

34.49 

5.93   35 

3635.56 

5.63  35.53 

5.79  35.51 

5.94 

35.48 

6.10j  36 

3736.54 

5.79  36.52 

5.95 

36.49 

6.11 

36.47 

6.271  37 

38'37.53 

5.94  37.51 

6.  11  137.48 

6.27 

37.45 

6.44    33 

3938.52 

6.10li38.49 

6.27 

38.47 

6.44 

38.44 

6.60    39 

40  39.51 

6.26  39.48|  6.43 

39.45 

6.60 

!39.42 

6.77   40 

|  

1] 

1  

4140.50 

6.41  i  40.47 

6.59 

40.44 

6.77 

J40.41 

6.94   41 

4241.48 

6.57,  41.451  6.75'  41.42 

6.92:  (41.  39 

7.11!  42 

43  42.47 

6.73  42.44!  6.91 

42.41 

7.10142.38 

7.281  43 

4443.46 

6.88:43.431  7.07 

43.40 

7.26143.36 

7.45    44 

4544.45    7.04:44.41    7.23 

44.38 

7.43 

44.35 

7.62 

45 

4645.43    7.20145.40   7.39 

45.37 

7.59 

45.34 

7.79 

46 

4746.42   7.35  46.391  7.55 

43.36 

7.76 

46.32 

7.96   47 

4847.41 

7.51:47.38    7.72 

47.34 

7.92  47.31 

8.13   48 

49  48.40 

7.67  '48.36 

7.88 

48.33 

8.09 

48.29 

8.30   49 

50  49.38 

7.82  49.35 

8.04 

49.32 

8.25 

49.28 

8.471  50 

ZT^pT 

Lat.tlDep. 

7Z 

Dep. 

Lat. 

»*L 

Lat.  +1 

CO 

5    81  DegJ\SOf  Deg. 

801  Deg. 

80}DegjS 

TRAVERSE  TABLE, 


5 

9  Deg. 

|9>  Deg.j9f  Deg. 

93  Deg. 

g 

51 

Lat. 

Dep. 

7.98 

Lat. 

50.34 

Dep.    Lat.,  Dep. 

8.20  50.30   8.42 

Lat.|Dep. 

50.26   8.64J 

51 

50.37 

52 

51.36 

8.13 

51.32 

8.36  51.29   8.58 

51.25i  8.8l!  52 

53 

52.35 

8.29 

52.31 

8.52152.27   8.75j|52.23j  8.98i  53 

54 

53.34 

8.45 

53.30 

8.68  53.26   8.91  53.22!  9.14   54 

55 

54.32 

8.60 

54.28 

8.84  54.25   9.08  54.211  9.31   55 

56 

55.31 

8.76 

55,27 

9.00  55.23   9.24  55.19:  9.48   56 

57 

56.30 

8.92 

56.26 

9.16156.22   9.41156.18;  9.65   57 

58 

57.29 

9.07 

57.25 

9.32  57.20   9.57157.16   9.82   58 

59 

58.27 

9.23 

58.23 

9.48  58.19   9.74  58.15   9.99   59 

60 

59.26 

9.39 

59.22 

9.6459.18   9.9059.1310.16   60 

61160.25 

9.54 

60.21    9.81  60.  16  10.07  '60.  12  10.33   61 

6261.24 

9.70 

61.19    9.97  61.  15  10.23  161.10  10.50|  62 

6362.22 
64  63.21 

9.86 
10.01 

62.18  10.13  62.14  10.40  162.09  10.67  j  63 
63.17  10.29  163.12  10.56  J63.08  10.84   64 

65  64.20 
6665.19 

10.17 
10.32 

64.1510.45164.1110.73 
65.14  10.61  165.09  10.89 

J64.06  11.01 
65.0511.18 

65 
66 

6766.18 

10.48 

66.1310.77  66.0811.06 

66.03!  11.  35 

67 

68 

67.16 

10.64 

67.12  10.93  67.07  11.22 

67.02ill.52 

68 

69 

68.15 

10.79 

68.1011.09  68.0511.39 

168.0011.69 

69 

70 

69.14 

10.95 

!  69,09  1L25  69.04  11.55 

68.99J11.85 

70 

71 

70.13 

11.11 

70.08 

11.41  70.0311.72 

69.97|l2.02 

71 

72 

71.11 

11.26 

71.06  11.57  71.01  11.88 

!70.96  12.  19 

72 

73J72.10  11.42 
74173.09  11.58 
75'74.08;11.73 

72.05  11.73  72.00  12.05  71.95  12.36 
73,04  11.89  72.99  12.211  72.93  12.53 
74.02  12.06  173.97  12.38  |73.92  12.70 

73 

74 
75 

76  75.06  11.  89;  75.01 

12.22  74.96  12.54 

74.90  12.87 

76 

77.76.05J12.05  76.00 

12.38  75.94  12.71 

75.89  13.04 

77 

7877.0412.20'  76.99 

12.54  76.93  12.87 

76.87  13.21 

78 

79  78.03  12.36!  '77.97 

12.70  77.9*  13.04 

77.8613.38 

79 

80  79.02 

12.51 

J78.96 

12.86  78.9013.20 

78.84  13.55 

80 

81 

80.0012.67  79.95 

13.02  79.89  13.37  79.83  13.72 

81 

82  80.99  12.83J  80.93 

13.18  80.8813.53 

80.8213.89 

82 

83  81.98  12.  9£ 

1  81.92 

13.34  81.86  13.70 

81.80  14.06 

83 

8482.97  13.14  82.91 

13.50  82.85  13.86 

82.7914.23 

84 

8583.95113.30.83.89 

13.66  83.83  14.03 

83.7714.39 

85 

86;84.94l  13.45  84.88 

13.82  84.82  14.19 

84.7614.56 

86 

87  85.93  13.61  85.87 

13.98  85.81  14.36  :85.74  14.73 

87 

88  86.92 

13.77  86.86 

14.15  86.79  14.52  86.73  14.90 

88 

89  87.9C 

13.92  87.84 

14.31  87.78  14.691  87.71  15.07 

89 

90j88.89 

i4.os 

!  88.83 

14.47  88.77  14.85  88.70  15.24 

90 

91 

89.88  14.24  89.82  14.63  89.75  15.02  ;89.69  15.41 

91 

92  90.87  14.39  90.80  14.79  90.74  15.18  90.67ll5.58 

92 

9391.86  14.55  91.79  14.95  91.72  15.351  91.66  15.75 

93 

9492.84  14.70  92.78il5.11  92.71  15.51!  92.6415.92 

94 

95  93.83  14.86  93.76'15.27  93.70  15.68  93.63,16.09 

95 

9694.82!15.02  94.75  15.43;  94.68  I5.84|i94.61  16.26 
9795.8lil5.17  95.74  15.59  95.67  16.011195.60  16.43 
9896.79  15.33  96.73  15.75  96.66  16.17  96.58  16.60 

96 
97 

98 

9997:78ll5.49  97;71  15.91  !97.64  16.34ll97.57  16.77 

99 

10( 

)98.7 

7  15.64.  98.  7C 

16.07  98.6316.50198.5616.93 

100 

t5 

Dep 

.  Lat 

.||Dep. 

Lat.|  Dep.  Lat 

!  

Dep.  Lat. 

t»5 

I 

81  DegJSO'Deg.  bo^Deg.'isOJDeg. 

S 

58 


TRAVERSE  TABLE. 


0 

lODeg.  jlO^Deg. 

lOpeg. 

lOfDeg. 

0 

ST 

Lat.  i  Dep.  1  Lat. 

.Dep.j  Lat. 

Dep. 

Lat. 

Dep. 

r 

i 

0.98 

0.17 

0.98 

0.18 

0.98 

0.18 

0.98 

0.19 

i 

2 

1.97   0.35     1.97 

0.36     1.97 

0.36 

1.96  0.37 

2 

3 

2.95i  0.52    2.95 

0.53,    2.95 

0.55 

2.95 

0.56 

2 

4 

3.94  0.69    3,94 

0.71 

3,93   0.73 

3.93 

0.75 

4 

5 

4.92   0.87 

4.92 

0.89 

4.92J  0.91 

4.91 

0.93 

K 

6 

5.91    1.04     5.90 

1.07 

5.90'  1.09 

5.89 

1.12 

6 

7 

6.89    1.22    6.89 

1.25 

6.88 

1.28 

6.88 

1.31 

8 

7.88    1.39,    7.87 

1.42 

7.87 

1.46 

7.86 

1.49 

f 

9 

8.86    1.56!    8.86 

1  60 

8.85 

1.64 

8.84 

1.68 

10 

9.85 

1.74    9,84 

1.78 

9.83 

1.82 

9.82 

1.87 

1C 

11 

10.83 

1.91 

10.82 

1.96 

10.82 

2.00 

10.81 

2.05 

u 

12 

11.82 

2.08  11.81 

2.14 

11.80 

2.19  11.79 

2.24 

12 

13 

12.80 

2.26  12.79 

2.31 

12.78 

2.37  12.77 

2.42 

13 

14  13.79 

2.43  13.78 

2.49 

13.77 

2.55  13.75 

2.61 

14 

15  14.77 

2.60'  14.76 

2.67 

14.75 

2.731114.74 

2.80 

15 

16 
17 

15.76 

16.74 

2.78115.74.  2.85 
2.95  16.73,  3.0S 

15.73 

16.72 

2.92JI15.72J  2.98 
3.10  16.70J  3.17 

16 
17 

18 

17.73 

3.13 

17.71 

3.20 

17.70 

3.28 

i  17.68 

3.36 

18 

19 

18.71 

3.30|18.70J  3.38 

'18.68 

3.46 

18.67 

3.54 

19 

20 

19.70 

3.47 

19.68 

3.56 

!  19.67 

3.64 

19.65 

3.73 

20 

21  20.68 

3.65 

20.66 

3.74 

20.65 

3.83  20.63 

3.92 

21 

22121.67 

3.82 

21.65',  3.91 

'21.63 

4.01 

21.61 

4.10 

"2 

2322.65 

3.99 

22.63!  4.09 

122.61 

4.19 

22.60 

4.29 

23 

24!23.64 

4.17 

23.62 

4.27 

123.60 

4.37 

23.58 

4.48 

24 

25,24.62)  4.34 

24.60 

4.45 

24.58 

4.56 

24.56 

4.66 

25 

26:25,61 

4.51 

25.59 

4.63 

'25.56 

4.74 

25.54 

4.85 

26 

27  26.59 

4.69 

26.57 

4.80 

26.55 

4.92 

26.53 

5.04 

27 

28 

£7.57 

4.86 

a?-  65    4.98  -27.53 

5.10 

27.51 

5.22 

28 

29 

28.56 

5.04 

28.54 

6.16i  28.51  1  5.28 

28.49 

5.41 

29 

30 

29.54 

5.21 

29.52 

5.34 

29.50!  5.47 

29.47 

5.60 

30 

31 

30.53 

5.38 

30.51 

5.52 

30.48 

5.65 

30.46 

5.78 

31 

32 

31.51 

5.56 

31.49 

5.69 

31.46 

5.83 

31.44 

5.97 

32 

33 

32.50 

5.73  S2.47 

5.87 

32.45 

6.01 

32.42 

6.16 

33 

34 

33.48 

5.90  33.46 

6.05  i33.43 

6.20  33.40 

6.34 

3_t 

35,34.47 

6.08134.44 

6,23 

34.41 

6.38  34.39 

6.53 

35 

36j35.45 
3736.44 

6.25,  35.43 
6.42'  36.41 

6.41 
6.58 

35.40   6,56i  35.37    6.71 
36.38   6.74  36.35;  6.90 

36 

3837.42 

6.60  37.39 

6.76 

37.36 

6.92 

37.33 

7.09 

38 

3938.41 

6.77i38.38 

6.94 

38.35 

7.11 

38.32    7.27 

39 

40  39.39 

6.95;39.36 

7.12 

39.33 

7.29 

;39.30 

7.46 

40 

i; 

L  

41 

40.38 

7.12  40.35   7.30 

40.31 

7.47 

40.28 

7.65 

41 

42 

41.36 

7.29 

41.33   7.47 

41.30 

7.65 

41.26 

7.83 

42 

43 

42.35 

7.47  42.31 

7.65 

42.28 

7.84 

42.25 

8.02 

43 

44 

43.33 

7.64 

43.30 

7.83 

43.26 

8.0*2 

43.23 

8.21 

44 

45 

44.32 

7.81  44.28 

8.01 

44.25 

8.20 

44.2  1> 

8.39 

45 

4645.30 

7.99  45.27 

8.19 

45.23 

8.38 

45.19 

8.58 

46 

47  46.29 

8.16  46.25 

8.36 

46.21 

8.57 

46.18 

8.77 

47 

48 

47.27 

8.34  47.23   8.54 

47.20|  8.75 

47.16 

8.95 

48 

49 

48.26 

8.51 

48.22   8.72 

48.18 

8.93 

48.14 

9.14 

49 

50 

49.24 

8.68 

;49.20;  8.90 

.      ' 

Eia 

9.11 

49.12 

9.33 

5Ci 

•M 

Dep. 

Lat. 

JDep. 

iLat. 

Dep. 

Lat. 

Dep. 

Lat. 

-  

1r 

.— 

80  Deg.J79fDeg.i79^Deg. 

79iDeg. 

b 

TRAVERSE  TABLE. 


d 

10  Deg. 

10]  Deji. 

mi)e^ 

lOJDeg.!  g 

r 

Lat. 

Dep. 

Lat.  Dep. 

Lat. 

Dep. 

Lat. 

en 
Dep.   f 

51 

50.23 

8.86 

50.19    9.08 

50.15 

9.29 

50.10 

9.51    51 

52 

51.21 

9.03 

51.17  9.25 

51,13 

9.48 

51.09 

9.70   52 

53 

52.19 

9.20 

52.15    9.-!> 

52.11 

9.66 

52.07 

9.89   53 

54 

53.18 

a.38 

53.14   *>.61 

53.10 

9.84 

53.05 

10.07   54 

55 

54.16 

9.55 

54.12   9.7;; 

54.08 

10.02 

54.03 

10.26   35 

56 

55.15 

9.72 

55.11    9.96 

55.06 

10.21 

55.02 

10.45   56 

57 

56.13 

9.90 

56.09  10.14 

56.0;: 

10.SL' 

56.00 

10.63   57 

58 

57.12 

10.07 

57.0?  10.32 

57  .03 

10.57 

56.98 

10.82   58 

59 

58.10 

10.25 

58.06*10.60 

58.01 

10.75 

57,96 

11.00   59 

60 

59.09 

10.42 

59.04  10.68 

5!'.  00 

10.93 

58.95 

11.19   60 

61 

60.07 

10.59 

60.03  10.85 

59.98 

11.12 

59.93 

11.38   61 

62 

61.06 

10.77 

61.01  11.03 

60.96 

11.30 

60.91 

11.56   62 

63 

62.04 

10.94 

61.9911.21 

61.0/> 

11.48 

61.89 

11.75   63 

64 

63.03 

11.11 

62.98-11.39 

62.93 

11.66 

62.88 

11.94   64 

65 

64.01 

11.29 

63.9611.57 

63.91 

11.85 

63.86 

12.12   65 

66 

65.00 

11.46 

64.95  11.74 

64.89 

12.03 

64.84 

12.31    66 

67 

65.98 

11.63 

65.9311.92 

65.88 

12.21 

85.82 

12.50   67 

68 

66.97 

11.81 

66.9112.10 

B6;86 

12.3}.: 

66.81 

12.68   68 

69 

67.95 

11.98 

67.9012.28 

67.84 

12.57 

67.79 

12.87   69 

70 

68.94 

12.16 

168.88  ;  12.46 

68.83 

12:76 

68.77 

13.06   70 

71 

69.92 

12.33 

69.87  12.63 

69.31 

12.94 

69.75 

13.24   71 

72 

70.91 

12.50 

70.8512.81 

70.79 

13.12 

70.74 

13.43   72 

73 

71.89 

12.68 

71.  83  12.39 

71.78 

13.30 

71.72 

13.62    73 

74 

72.88 

12.86 

72.8213.17 

72.7 

13.4S 

72.70 

13.80   74 

75 

73.86 

13.02 

73.80  13.35 

72.74 

"13.67 

73.68 

13.99    75 

76 

74.8o 

13.20 

74.79  13.52 

74.73 

13.85 

74.67 

14.18   76 

77 

75.8- 

13.37 

75.77'  IS.  70 

75.71 

14.03 

75.65 

14.36   77 

78 

76.8- 

13.54 

76.76:13.88 

76.6S 

14.21 

76.63 

14.55    78 

79 

77.  8U 

13.72 

77.74'14.06 

77.66 

14.40 

77.61 

14.74   79 

80 

78.78 

13.89 

78.  72|  14.24 

78  .€e 

14.58 

78.60 

14.92   80 

81 

79.77 

14.07 

79.71  14.41 

79.64 

14.76 

79.58 

15.11    81 

82 

80.75 

14.24 

80.69  14.59 

30.63 

14.94 

80.56 

15.29    82 

83 

81.74 

14.41 

81.6814.77 

81.61 

15.13 

81.54 

15.48    83 

84 

82.72 

14.59 

82.66i  14.95 

82.59 

15.31 

82.53 

15.67  €4 

85 

83.71 

14.76 

83.6415.13 

83.58 

15.49 

83.51 

15.85    85 

86 

84.69 

14.93 

84.6315.30 

84.56 

15.67 

84.49 

16.04   86 

87 

85.68 

15.11 

85.61:15.48 

85.54 

15.85 

85.47 

16.23.  87 

88 

86.66 

15.28 

86.60(15.66 

86.55 

16.04 

86.46 

16.4J'  88 

89 

87.65 

15.45 

87.58>15.84 

87.51 

16.22 

87.44 

16.60   89 

90 

88.63 

15.63 

88.56  16.01 

88.49 

16.40 

88.42 

16.79;  90 

91 

89.62 

15.80 

89.  55'  16.  19 

89.48 

16.58 

89.40 

16.97!  91 

92 

90.60 

15.98 

90.53'  16.37 

90.46 

16.77 

90.39 

17.16   92 

93 

91.59 

16.15 

91.52  16.6c 

91.44 

16.95 

91.37 

17.35   93 

94 

92.57 

16.32) 

92.50:16.73 

92.4317.13 

92.35 

17.53   94 

95 

93.56 

16.50i 

93.48il6.9C 

93.41J17.31 

93.33 

17.72:  95 

96 

94.54 

16.  67;i94.47  17.08 

94.39 

17.4:' 

94.32 

17.91   96 

97 

95.53 

16.84i  95.45ll7.26 

95.38 

17.68 

95.30 

18.091  97 

98196.51 

17.02!  96.44  17.44 

96.36 

17.86 

06.28 

18.281  98 

99 

97.50 

17.19 

97.42  17.62 

97.34 

18.04 

97.26 

18.47    99 

100 

98.4? 

17.36 

98.40  17.79 

98-33 

18.22 

98.25 

18.65jlOO 

t8 

Dcp. 

Lat. 

Dep.  Lat. 

D^pT 

Lat. 

Dep. 

1^7 

3 

80  Deg. 

79-tDeg.] 

79iDeg. 

79iDeg,p 

TRAVERSE  TABLE. 


e 

1 

11  Deg. 

HJDeg. 
Lat.  Dep. 

nil 

Lat. 

Deg. 
Dep.j 

ll£Deg. 

? 

Xjtit 
* 



Lat. 

Dep. 

.  1 

0.98J  0.19J!  0.98!  0.20 

0.98 

0.20 

0.98 

0.20 

1 

2 

1.961  0.38 

1.96!  0.39 

1.96 

0.40 

1.96 

0.41 

2 

3 

2.94!  0.57' 

2.94   0.59 

2.94 

0.60 

2.94 

0.61 

3 

4 

3.93  0.76 

3.92  0.78 

3.92 

0.80 

3.92   0.82 

4 

5 

4.91   0.95! 

4.90  0.98 

4.90 

.00 

4.90    1.02 

5 

6 

5.89    1.141 

5.88     .17 

5.88 

.20 

6.87 

1.22 

6 

7 

6.87   1.34 

6.87     .37 

6.86 

.40 

6.85 

1.43i     7 

8 

7.85,  1.53 

7.85     .56 

;  7.84 

.59 

7.83 

1.63 

8 

9 

8.83 

1.72 

8.83     .76 

I  8.82 

.79 

8.81 

1.83 

9 

10 

9.82    1.911 

9.81      .95 

I  9.80 

.99 

9.79 

2.04 

10 

1110.80   2.10 

10.79   2.15 

10.78 

2.19 

10.77 

2.24 

11 

1211.78   2.29 

11.77   2.34 

11.76 

2.39 

11.75 

2.44 

12 

1312.76   2.48 

12.75    2.54 

12.74 

2.59 

12.73 

2.65 

13 

1413.74   2.67 

13.73   2.73 

13.72 

2.79 

13.71 

2.85'  14 

1614.72J  2.86 

14.71    2.93 

14.70 

2.99 

14.69 

3.06 

15 

16!  15.71J  3.05 

15.69    3.12 

15.66 

3.19 

15.86 

3.26 

16 

17  16.691  3.24 

16.67   3.32 

16.66 

3.39 

16.64 

3.46 

17 

1817.67'  3.43 

17.65   3.51 

17.64 

3.59 

17.62 

3.66 

18 

1918.65!  3.63 

18.63   3.71 

18.62 

3.79 

18.60 

3.87 

19 

2019.63i  3.82 

1S.62   3.90 

19.60 

3.99 

19.58 

4.07 

20 

I                ! 

2l!20.6l|  4.01  J20.60   4.10!  20.58 

4.19 

20.56 

4.28 

21 

22:21.60   4.20  121.58   4.29;  21.56 

4.39 

21.54 

4.48 

22 

2322.581  4.39 

22.56   4.49 

22.64 

4.59 

22.56 

4.68 

23 

24:23.56!  4,59,  23.54  4.68 

23.52 

4.78 

23.50 

4.89 

24 

25:24.64 

4.7?  124.52   4.88 

24.50 

4.98 

24.48 

5.09 

25 

2625.52 

4.96 

25.50   5.07 

25.48 

5.18 

25.46 

5.30 

26 

27  26.50 

5.15 

26.48   5.27 

26.46 

5.38 

26.43 

5.50 

27 

2827.49 

5.34i27.46   5.46:27.44 

5.58 

27.41 

5.70 

28 

2928.47 

5.53  28.44   5.66 

28.42 

5.78 

28.39 

5.91 

29 

3029.45 

5.72  29.42   5.85 

29.40 

5.98 

29.37 

6.11 

30 

~JJ 

30.43 

5.92 

30.40   6.05 

30.38 

6.18 

30.35 

6.31 

31 

32 

31.41 

6.11; 

31.39    6.24 

31.36 

6.38 

31.33 

6.52 

32 

33 

32.39 

6.30 

32.37;  6.44 

32.34 

6.58 

32.31 

6.72   331 

34 

33.38 

6.49 

33.35!  6.63 

33.32 

6.78 

33.29 

6.92 

34 

35 

34.36 

6.68 

34.33;  6.83 

34.30 

6.98 

34.27 

7.13 

35 

36 

35.34J  6.87  35.3L  7.02 

35.28 

7.18 

35.26 

7.33 

36 

37 

36.32!  7.06 

36.29;  7.22 

36.26 

7.38 

36.22 

7.53 

37 

38 

37.30 

7.26 

37.271  7.41 

37.24 

7.58 

37.20 

7.74 

38 

39 

38.28 

7.44  38.26   7.61 

38.22 

7.78 

38.18 

7.94 

39 

40 

39.27 

7.63  39.23    7.80  39.20 

7.97 

39.16 

8.15 

40 

____ 

j  u  , 

__ 



_____ 



4140.25 

7.82 

40.21!  8.00 

40.18 

8.17 

40.14 

8.35 

41 

4241.23 

8.01 

41.19;  8.19 

41.16 

8.37 

41.12 

8.55 

42 

4342.21 

8.20 

42.171  8.39 

42.14 

8.57 

42.10 

8.76 

43 

4443.19 

8.40 

43.15!  8.58 

43.12 

8.77 

43.08 

8.96 

44 

4544.17 

8.59  44.14   8.78 

44.10 

8.97 

44.06 

9.16 

45 

4645.15 

8.78 

45.12   8.97 

45.08 

9.17 

45.04 

9.37 

46 

4746.14   8.97 

46.10:  9.17 

46.06 

9.37 

46.02 

9.57 

47 

4847.12.  9.16 

47.08!  9.36 

47.04 

9.57 

46.99 

9.78 

48 

4948.10'  9.35l48.06!  9.56 

48.02 

9.77 

47.97 

9.98 

49 

5049.08;  9.64J49.04   9.75 

49.00 

9.97 

48.95 

10.18 

50 

^  Dep.  Lat.; 

Dep.i  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

CO 

5    79  Deg. 

782  Deg. 

78_  DegJ 

781~Deg. 

s. 

TRAVERSE  TABLE, 


0HDeg. 

HiDeS 

llfDeg. 

HfDeg.ig 

»-«  *  -  •• 

,        !    !•••.•!•          ..          • 

1    •        *    "  •— 

'  55* 

r*"1  Lat.  Dep. 

Lat.|Dep. 

Lat.  !  Dep. 

Lat.lDep.   f* 

- 

i_,  _   —  .  •    ,    JLUJ 

L  -rL  ._._       j            

j-.j  I   

5150.06J  9.73 

50.02'  9.95 

49.9810.17 

49.9310.39   51 

5251.04   9.92 

51.0010.14 

50.9610.37 

50.91  !  10.59   52 

53  52.03]  10.  11 

51.98  10.34 

51.9410.57 

61.8910.79   63 

5453.01110.30 

52.96  10.53 

52.92  10.77 

52.87:11.00   54 

55I53.99!  10.49 

53.94  10.73 

53.90  10.97 

53.8511.20   55 

5654.97:10.69 

64.92  10.93 

64.88  11.16 

54.8311.40   56 

5755.9510.88 

55.9011.12 

55.  86  11.36 

55.81  11.61   57 

6856.9311.07 

56.89  11.32 

56.8411.56 

66.78111.81    58 

5957.9211.26 

57.8711.51 

57.82  11.76 

57.76 

12.01   59 

SO  58.  90  11.  45 

58.85  11.71 

58.8011.96 

58.74 

12.22   60 

61  59.88  11.64 

59.8311.90 

59.78J12.16 

59.72 

12.42   61 

6260.8611.83 

60.81  12.10 

60.76  12.36 

60.70 

12.63   62 

63  61.84  12.02 

61.79  12.29 

61.74  12.56 

61.68 

12.83   63 

6462.8212.21 

62.77  12.49 

62.72:12.76 

62.66 

13.03   64 

65  63.81  12.40 

62.75  12.68 

63.7012.96 

63.64|  13.24   65 

66  64.79  12.59 

64.73  12.88 

64.68  13.16 

64.62  13.44   66 

67  65.77  12.78 

65.71  13.07 

65.  66i  13.36 

65.6013.64   67 

68  66.75  12.98 

66.69  13.27 

66.63J  13.56  66.58;  13.86   68 

6967.7313.17 

67.67  13.46 

67.61J13.76 

67.55  14.051  69 

7068.71  13.36 

68.66tl3.66 

68.  59  j  13.  96 

68.53jl4.25j  70 

71  69.70  13.55 

69.64  13.85 

69.5714.16 

69.51  14.46    71 

72  70.68  13.74 

70.62  14.05 

70.5514.35 

70.49  14.66!  72 

73  71.66  13.93 

71.60  14.24 

7  1.53  114.55 

71.47  14.871  73 

7472.6414.12 

72.58  14.44 

72.51  i  14.  75 

72.45  15.07    74 

75  73.62  14.31 

73.66  14.63 

73.49i  14.95 

73.4315.27'  75 

76  74.60  14.50 

74.64  14.83 

74.47  i  15.  15 

74.41 

15.481  76 

77  75.59  14.69 

75.52  15.02 

75.45i  16.35 

75.39 

15.68J  77 

78  76.57  14.88 

76.5015.22 

76.43i  15.55 

76.37 

15.88|  78 

79  77.55  15.07 

77.48  15.41 

77.41  i  15.  75 

77.34 

16.091  79 

80  78.63  15.26 

78.4615.61 

78.39J  15.95 

78.32 

16.29J  80 

81  79.51  15.46 

79.44  15.80 

79.37  16.15 

79.30 

l€.49i  81 

82  80.49  15.65 

80.4216.00 

80.35  16.35 

80.28 

16.70J  82 

83  81.48  15.84 

81.41  16.19 

81.33  16,55 

81.26 

16.90   83 

84  82.46  16.03 

82.39  16.39 

82.31  16.75 

82.24 

17.11    84 

85  83.44  16.22 

83.37  16.58 

83.29  16.95 

83.22 

17.31    85 

86  84.42  16.41 

84.35  16.78 

84.27  17.16 

84.20 

17.51    86 

87  85.40  16.60 

85.33  16.97 

85.25  17  36 

85.18 

17.72   87 

8a  86.38  16.  79 

86.31  17.17 

86.23  17.64 

86.16 

17.92   88 

89  87.36  16.98 

87.29  17.36 

87.21J17.74 

87.14 

18.12   89 

90  88.35  17.17 

88.2717.56 

88.19117.94 

88.11 

18.33:  90 

9189.3317.36 

89.26  17.75 


89,17i  18.  14 

89.09 

18.531  91 

92'90.31  17.55 

90.23  17.95 

90.15J18.34 

90.07 

18.74   92 

9391.2917.75 

91.21  18.14 

91.13  18.54 

91.06 

18.94   93 

9492.2717.94 

•92.19  18.34 

92.11  18.74 

92.03 

19.14   94 

9593.2518.13 

93.17  18.53 

93.09  18.94 

93.01  19.35   95 

96  94.24  18.32 

94.16  18.73 

94.07  19.14 

93.99  19.55   96 

9795.2218.51 

95.14  18.92 

95.05  19.34 

94.9719.75   97 

9896.2018.70 

96.1219.12 

96.031  19.54 

96.95 

19.96   98 

99  97.18  18.89 

97.1019.31 

97.01  '19.  74 

96.9320.16   99 

10098.16,19.08 

98.08  19.51 

97.99  19.94 

97.9020.36100 

*J   Dep.j  Lat. 

Dep.   Lat. 

Dep.  Lat 

Dep.  1  Lat.  .g' 

ft    79  Deg. 

78£Deg. 

78£Deg.i 

,78*  Deg.  P 

TRAVERSE  TABLE. 


0 

12  Deg. 

12i  Deg. 

12iDeg. 

12|Deg.  0 

«j" 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

1 

0.98 

0.21 

0.98 

0.21 

0.98 

0.22    0.98 

0.22 

i 

2 

1.96   0.42 

1.95 

0.42 

1.95 

0.43    1.95 

0.44 

2 

3 

2.93   0.62 

2.93 

0.64 

2.93 

0.65    2.93 

0.66 

3 

4 

3.91   0.83 

3.91 

0.85 

3.91 

0.87    3.90 

0.88 

4 

5 

4.89i     .04 

4.89 

.06 

4.88 

1.08    4.88 

1.10 

5 

6 

5.87!     .25 

5.86 

.27 

5.86 

1.30    5.85 

1.32 

6 

7 

6.85      .46 

6.84 

.49     6.83 

1.52    6.83 

1.54 

7 

8 

7.83 

.66 

7.82 

.70    7.81 

1.73!  7.80 

1.77 

8 

9 

8.80 

.87 

8.80 

.91     8.79 

1.95     8.78 

1.99     9 

10 

9.78 

2.08 

9.77 

2.12 

9.76 

2.16!  9.75 

2.21    10 

iii 

10.76 

2.29  10.75 

2.33 

10.74 

2.38!l0.73   2.43 

11 

121 

11.74 

2.49 

11.73 

2.55J  11.72 

2.60  11.70 

2.65 

12 

13i  12.72   2.70 

12.70 

2.76  12.69 

2.81  ;i2.68 

2.87 

13 

14113.69;  2.9l!l3.68 
151  14.67    3.12(14.66 

2.97 
3.18 

13.67 
14.64 

3.03  13.65 
3.25  14.63 

3.09 
3.31 

14 
15 

1615.65 

3.33 

15.64 

3.39 

15.62 

3.46  15.61 

3.53 

16 

n'16.63    3.53 

16.61 

3.61 

16.60 

3.68.  '16.58 

3.75 

17 

18'17.61    3.74 

17.59 

3.82 

17.57 

3^0  17.56 

3.97 

18 

19 

18.58   3.95 

18.57 

4.03 

18.55 

4.11  18.63   4.19 

19 

2019.56J  4.16 

19.54 

4.24 

19.53 

4.33|'l9.51 

4.41 

20 

2L20.54 

4.37 

20.52 

4.46 

20.50 

4.55 

20.48!  4.63   21 

2221.52 

4.57 

21.50 

4.67 

21.48 

4.76  21.46 

4.86   22 

2322.60 

4.78 

22.48:  4.88 

22.45 

4.98  22.43 

6.08   23 

2423.48 

4.99 

23.45J  5.09 

23.43 

5.19,23.41 

5.30   24 

2524.45;  5.20 

24.43   5.30 

24.41 

5.41;  124.38 

5.52   25 

2625.43   5.41 
2726.41    5.61 

25.41    5.52 
26.39|  5.73 

25.38 
26.36 

5.63 
5.84 

25.36   5.74-  26 
26.33   5.96   27 

2827.39 

5.82 

27.36 

5.94*  27.34 

6.06 

27,31 

6.18i  28 

29:28.37 

6.03 

28.34 

6.15 

28.31 

6.28 

28.28 

6.40:  29 

30;29.34 

6.24 

29.32 

6.37 

29.29 

6.49 

29.26 

6.62:  30 

31  30.32 

6.45130.29 

6.58  30.271  6.71 

30.24 

6.8-4   31 

32  31.30 

6.65 

31.27    6.79 

31.24 

€.93 

31.21 

7.06   32 

33  32.28 

6.86 

32.25 

7.00 

32.22 

7.  14  32.19 

7.28   33 

3433.261  7.07 

33.23 

7.21 

33.19 

7.36 

33,16 

7.50  34 

3534.24   7.28 

34.20   7.43 

34.17 

7.68)34.14 

7.72   35 

3635.21    7.48 

35.18    7.64 

35.15    7.79  35.11    7.951  36l 

3736.19    7.69 

36.16 

7.85 

36.12 

S.Oli  36.09 

8.17;  37 

3837.171  7.90 

37.13 

8.06 

37.10!  8.22IJ37.06 

8.39!  38 

3938.151  8.11 

38.11 

8.27 

38.08i  8.44138.04 

8.61    39 

40 

39.131  8.32 

39.09 

8.49 

39.05 

8.66 

39.01 

8.83   40 

4140.10   8.52 

40.07 

8.70 

140,03 

8.87 

39.99 

9.05   41 

4241.08   8.73 

41.04   8.91 

41.00 

9.09 

40.96 

9.27   42 

4342.06    8.94 

42.02    9.12 

41.98 

9.31 

41.94 

9.49   43 

4443.04!  9.15 

43.00   9.34 

42.96 

9.52 

42.92 

9.7L  44 

4544.02   9.36 

43.98!  9.56 

43.93   9.74!  43.89 

9.93   45 

4644.99J  9.56 

44.95   9.76 

44.91)  9.96  44.87 

10.15   46 

4745.97 

9.77 

45.93)  9.97 

45.8910.17  45.8410.37'  47 

4846,95   9.98 

46.91110.18 

46.86:  10;39  46.82 

10.59   48 

4947.9310.19 

47.88  10.40 

47.84  10.61!  47.79  10.81   49 

5048.91  10.40 

48.86J10.61 

49.81 

10.82  48.77'  11.03J  60 

^  Dep.  1  Lat. 

£"  
Q  !  78  Deg. 

.Dep.  1  Lat,  Dep. 

Lat.; 

Dep. 

Lat. 

"02 

:77fDeg. 

177*1 

DegJ 

77iDeg.O 

TRAVERSE  TABLE. 


0 

12  Deg. 

12iDeg. 

12iDeg. 

12fDeg. 

C 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

51 

49.89 

10.60 

49.84 

10.82 

49.79 

11.04 

49.74:11.26 

51 

52 

50.86 

10.81 

50.82  11.03 

50.77 

11.25 

50.7211.48 

52 

53 

51.8411.02 

51.79  11.25 

51.74 

11.47 

51.6911.70 

53 

54 

52.8211.23  52.77 

11.46 

52.72 

11.69 

52.67 

11.92 

54 

55 

53.80  11.44| 

53.75  11.67 

53.70 

11.90 

53.64 

12,14 

55 

56 

54.78 

11.64 

54.72 

11.88 

54.67 

12.12 

54.62 

12.36 

56 

57 

55.75 

11.85 

55.70 

12.09 

55.65 

12.34 

55.59 

12.58 

57 

58 

56.73 

12.06 

56.68 

12.31 

56.63 

12.55 

56.  57  112.80 

58 

59 

57.71 

12.27 

57.66 

12.52 

57.60 

12.77 

57.55 

13,02 

59 

60 

58.69  12.47 

58.63 

12.73 

58.58 

12.99 

58.52 

13.24 

60 

61 

59.67  12  68 

59.61 

12.94 

59.55 

13.20 

59.50 

13,46 

61 

62 

60.65ll2.89 

60.59 

13.16 

60.53 

13.42 

60.47 

13.68 

62 

63 

61.6213.10 

61.57 

13.37 

61.51 

13.64 

61.45  13.90 

63 

64 

62.60113.31 

62.54 

13.58 

62.48 

13.85 

62.42il4.12 

64 

65 

63.58  13.51 

63.52 

13.79 

63.46 

14.07 

63.40!  14.35 

65 

66 

64.56  13.72 

64.50 

14.00 

64.44 

14.29 

64.37 

14.57 

66 

67 

65.54  13.93 

65.47 

14.22 

65.41 

14.50 

65.35  14.79 

67 

68 

66.5114.14 

66.45 

14.43 

66.39 

14.72 

66.32  15.01 

68 

69 

67.49  14.35 

67.43 

14.64 

67.36 

14.93 

67.30  15.23 

69 

70 

68.47 

14.55 

68.41 

14.85 

68.34 

15.15 

68.27;  15.45 

.70 

•71 

69.45 

1-176 

69,38 

15.06 

69.32 

15.37 

69.25 

15.67 

71 

72 

70.43 

14.97 

70.36 

15.28 

70.29 

15.58 

70.22 

15.89 

72 

73 

71.40 

15.18 

71.34 

15.49 

71.27 

15.80 

71.20;i6.11 

73 

74 

72.38 

15.39|72.32 

15.70 

72.?5 

16.02 

72.  18!  16.33 

14t 

75 

73.36 

15.  59  j  73.29 

15.91 

73.22 

16.23 

73.15 

16.55 

75 

76 

74.34 

15.80*74.27 

16.13 

74.20 

16.45 

74.13 

16.77 

76 

77 

75.32 

16.0lh5.25 

16.34 

75.17 

16.67 

75.1016.99 

ii 

78 

76.30 

16.22  1  76.22 

16.55 

76.  lo 

16.88 

76.08  17.21 

78 

79 

77.27 

16.43  '7.20 

16.76 

77.13 

17.10 

77.05 

17.44 

79 

80 

78.25 

16.63|J78.18 

16.97 

78.10 

17.32 

78.03 

17.66 

80 

81 

79.23 

16.84  79.16 

17.19 

79.08 

17.53!  b9.00 

17.8S 

81 

82 

80.21 

17.05  80.13 

17.40 

80.06 

17.75: 

79.9818.10 

82 

83 

81.19 

17.26  81.11 

17.61 

81.03 

17.96j 

80.95  18.32 

83 

84 

82.16 

17.46  82.09 

17.82 

82.01 

18.1R| 

81.93  18.54 

84 

85 

83.14 

17.67  83.06 

18.04 

82.99 

18.40 

82.90 

18.76 

85 

86 

84.12 

17.88  84.04 

18.25 

83.96 

18.61 

83.88  18.98 

86 

87 

88 

85.10 
86.08 

18.09  85.02 
18.30  86.00 

18.46 
18,67 

84.94 
85.91 

18.83 
19.05 

84.85  19.20 
85.8319.42 

87 

88 

89 

87.06 

18.50  86.9? 

18.88 

86.89 

19.26 

86.81 

19.64 

89 

90 

88.03 

18.71H87.9S 

19.10 

87.87 

19.48 

87.78 

19.86 

90 

91 

89.01 

18.92  88.93 

19.31 

88.84 

19,70 

88.76 

20.08 

91 

92 
S3 

89.99 
90.97 

19.13  89.91 

19.34  90.88 

19.52 
19.73 

89.82 
90.80 

19.91, 
20.13 

89.73 
90.71 

20.30 
20.52 

92 
93 

94 

91.95 

19.54  91.86 

19.94 

91.77 

20.35  91.68 

20.75 

94 

95 

92.92 

19.75  92.84 

20.16 

92.75 

20.56  92.66120.97 

95 

96 

93.90 

19.96  93.81 

20.37 

93.72 

20.78;  93.  63121.  19 

96 

97 

94.88 

20.17  94.79 

20.58 

94.70 

30.99  94.61  21.4] 

97 

98 

95.86 

20.38  |95.77 

20.79 

95.68 

21.21i95.5821.63 

99 
100 

96.84 
97.81 

20.58 
20.79 

96.75 

97.72 

21.01 
21.22 

96.65 
97.63 

21.43  96.56  21.85 
21.64  97.5322.07 

99 
100 

S3 

Dep.   Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

•*J 

P 

78  Deg. 

l77£Deg, 

77iDeg.;!77iDeg. 

64 


TRAVERSE  TABLE. 


t 

13  Deg 

13;  Deg.  1  13^  Deg. 

I^Deg'o 

c 

La 

Dep 

Lat.  Dep.    Lat.  Dep. 

Lat.  Dep 

r 

0.9 

0.23 

0.97  0.23    0.97  0.23 

0.97   0.& 

i   i 

1.9 

0.4 

1.95   0.46     1.95  0.47 

1.94  0.4f 

5     2 

2.9 

0.6 

2.92   0.69    2.92  0.70 

2.91   0.71 

3 

3.9C 

0.90 

3.89   0.92    3.89   0.93 

3.89   0.95     4 

4.8 

1.1 

4.87    1.15    4.86    1.17 

4.86   1.19     5 

5.8 

1.3 

5.84    1.38    5.83    1.40 

5.83   1.43     6 

6.8 

l.c 

6.81    1.60;    6.81    1.63 

6.80   1.66     7 

7.80 

1.1 

7.79    1.83    7.78   1.87 

7.77    1.901     8 

8.7 

2.02 

8.76   2.06    8.75   2.10 

8.74   2.14J     9 

1 

9.7 

2.2 

9.73   2.29;    9.72   2.33 

9.71   2.38    10 

10.7 

2.47 

10.71    2.52'  10.70   2.57 

10.68   2.61    11 

11.6 

2.70 

11.68   2.751  11.67   2.80 

11.66   2.85;    2 

12.6 

2.92 

12.65   2.98  12.64   3.03 

12.63   3.09     3 

13.6 

3.15 

13.63   3.21   13.61    3.27 

13.60   3.33     4 

14.6 

3.37 

14.60   3.44;  14.59   3.50 

14.57   3.571    5 

15.59 

3.60 

15.57   3.67  15.56   3.74 

15.54   3.80     6 

16.57 

3.82 

16.55    3.90  16.53   3.97 

16.51    4.04     7 

17.54 

4.05 

17.52    4.131  17.50  4.20 

17.48   4.281'   8 

18.51 

4.27 

18.49   4.35!  18.48   4.44 

18.46   4.52 

2< 

9.49 

4.50 

19.47   4.58!  19.45   4.67 

19.43   4.75 

20 

21 

0.46 

4.72 

20.44   4.81  20.42   4.90 

20.40   4.99 

21 

22 

1.44 

4.95 

21.41    5.0421.39   5.14 

21.37   5.23 

22 

23 

2.41 

5.17 

22  39    5.27  22.36   5.37 

22.34   5.47 

23 

24 

23.38 

5.40 

23.36   5.50  23.34   5.60 

23.31   5.70   24 

25 

24.36 

5.62 

4.33   5.73J  24.31    5.84 

24.28   5.94J  25 

26 

5.33 

5.85 

5.31    5.96125.28    6.07 

25.25    6.18:  26 

2' 

6.31 

6.07 

6.28   6.19 

26.25   6.30 

26.23   6.42   27 

28 

7.28 

6.30 

7.25    6.42 

127.23   6.54 

27.20   6.66 

28 

2* 

8.26 

6.52 

8.23  6.65 

28.20!  6.77 

28.17'  6.89 

29 

30 

9.23 

6.75 

9.20   6.88 

29.17    7.00 

29.14J  7.13 

30 

31 

J0.21 

6.97 

30.17   7.11 

30.14   7.24 

30.11    7.37 

SI 

32 

1.18 

7.20 

1.15   7.33 

31.12    7.47 

31.08    7.61 

32 

31 

2.15 

7.42 

2.12   7.56 

32.09    7.70 

32.05   7.84 

33 

34 

J3.13 

7.65 

33.09   7.79 

33.06    7.94 

33.03   8.08,  34 

35 

J4.10 

7.87 

34.07   8.02 

34.03   8.17 

34.00   8.32   So 

36 

5.08 

8.10 

35.04   8.25 

35.01    8.40 

34.97!  8.56   36 

>7 

6.05 

8.32 

6.02   8.48 

35.98   8.64 

35.94   8.79 

37 

38 

7.03 

8.55 

6.99   8.71 

36.95   8.87 

36.91    9.03 

38 

39 

8.00 

8.77 

7.96    8.94! 

37.92    9.10! 

37.88    9.27 

39 

40 

8.97 

9.00 

8.94    9.17J 

38.89   9.34) 

38.85    9.51 

40 

41 

9.95 

9.22 

9.91    9.40;'39.87   9.57 

39.83J  9.751  41 

42 

K).92 

9.45 

10.88   9.63;40.84   9.80 

40.  80  "9.  98   42 

43 

.90 

9.67 

.86    9.86:41.81  10.041 

1.7710.22   43 

44 

.87 

.90 

12.8310.08  42.78  10.27  42.74  10.46    44 

45 

.85 

0.12 

13.8010.31  43.7610.51 

13.71  10.70!  45 

46 
47 
48 

.82 
.80 
.77 

0.35 
.57 

.80 

14.  78  10.  54  44.7310.74 
5.7510.77  45.7010.97 
.72  11.00  46.67  11.21 

14.68  10.93!  46 
15.65'  11.  17!  47 
16.62  11.  41  j  48 

49 

.74 

.02 

.7011.23 

47.6511.44 

17.6011.651  49 

60 

.72 

.25 

8.6711,46 

48.6211.67 

18.57  11.881  50 

ep. 

•    ,~ 

at. 

epj  Lat. 

DepJ  Lat. 

^"E^r 

77  Deg. 

6*Deg. 

76£Deg. 

r6iDeg.|Q 

. 


TRAVERSE  TABLE. 


g 

ISDeg. 

ISjDeg. 

ISjDeg.^SIDeg.  g 

*  " 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.|Dep.|j  Lat. 

Dep.|  r 

5149.69 

11.47 

49.64 

11.691  49.59;11.91l!49.54 

12.12   51 

5250.67 

11.70 

50.62 

11.921:50.5612.14  50.51 

12.36J  52 

5361.6411.92 

51.59 

12.15  51.  54!  12.371  5U48 

12.60!  53 

5452.62il2.15 

52.56  12.38  52.51  ;i2.61;  52.45 

12.84'  54 

5553.5912.37 

53.54  12.61 

53.48:12.84:53.42 

13.07|  55 

5654.56:12.60 

54.51  12.84  :54.45|13.G7!  54.40 

13.31   56 

57  55.54 

12.821  55.48113.06  55.431  13.31  55.37 

13.55   57 

58  56.51 

13.05  p56.46ll3.29  56.40  13.54  56.34 

13.79   58 

59  57.49 

13.27 

7.43113.52  57.37ilS.77  57.31 

14.02   59 

6058.46 

13.50 

8.40 

13.75 

58.34:14.01  58.28 

14.26    60 

•6159.44 

18.72 

9.38 

13.98 

i 
59.31  J14.241, 

59.25 

14.50   61 

62  60.41 

13.95 

60.351  14.21  i60.29ll4.471  60.22 

14.74 

62 

63  61.39 

14.17 

1.32:14.44,61.2614.71 

61.19 

14.97 

63 

64  62.36 

14.40 

2.30114.67162.2314.94 

62.17 

15.21 

64 

65  63.33 

14.62 

3.27 

14.90  63.2015.17 

63.14 

15.45 

65 

66  64.31 

14.85 

64.24 

15.13  64.18  15.41 

64.11 

15.69 

66 

67  65.28 

15.07 

65.22 

15.36  65.15  15.641 

65.08 

15.93 

67 

68  66.26 

15.30 

66.19 

15.59  66.12  15.87!  ;66.05 

16.16 

68 

6967.23 

15.52 

67.16 

15.81J  67.09  16.111 

67.02 

16.40 

69 

70  68.21 

15.75 

68.14 

16.04  68.07  16.34; 

67.99 

16.64 

70 

71  69.18 

15.97 

69.11 

16.27 

69.04  16.57; 

68.9" 

16.88J  71 

7270.15 

16.20 

70.08 

16.50 

70.01  16.81 

69.94 

17.11 

72 

7371.13 

16.42 

71.0616.73  TO.98  17.04 

70.91 

17.35 

73 

74  72.10  16.65 

72.03!  16.96  71.9617.28 

71.88 

17.59 

74 

75  73.08  16.87 

73.00  17.19  :72.93  17.50: 

72.85 

17.83 

75 

7674.0517.10 

73.9817.42173.9017.74 

73.82 

18.06 

76 

77  75.03117.32 
7876.0017.55 

74.95J17.65!  74.87  17.98, 
75.92  17.88:  75.84  18.21 

74.79 
75.76 

18.30 
18.54 

77 

76 

79:76.98117.77 
8077.9518.00 

76.9018.11 

77.87  18.34 

76.8218.44 
77.7918.68 

76.74 
77.71 

18.78 
19.01 

7 
80 

—  I  1  
81J78.92  18.22 

78.8418.57 

;78.76  18.91 

78.68 

19.25 

81 

82!79.90i  18.45 

79.82  18.79 

79.73  19.14 

79.65 

19.49 

82 

8380.87ll8.67 

80.79 

19.02 

80.71  19.38 

80.62 

19.73 

83 

84  81.  85|  18.90 

81.76  19.25 

81.68  19,61 

81.59 

19.97 

84 

85! 

82.82!19.12 

82.74!  19.48 

i82.65  19.84' 

82.56  20.20 

85 

86!83.80  19.35 

83.7lil9.71 

83.62  20.08 

83.5420.44 

86 

87  84.77  19.57 

84.68!  19.94 

84.6020.31 

84.51  20.68 

87 

88  85.  74'  19.80 

85.66!20.17  85.57|20.54 

85.48  20.92 

88 

89  86.72:20.02 

86.63!20.40:  86.54:20.78 

86.4521.15 

89 

90 

87.69  20.25 

87.60 

20.63  i87.  51  21.01 

87.4221.39J  90 



--_._, 



rt 

91 

88.67 

20.47 

88.58 

20.86  88.49  21.24' 

88.39 

21.63 

91 

92 

89.6420.70 

89.55121.09  89.46i21.481 

89.3621.87 

92 

93 

90.62120.92 

90.52J21.32  90.43j21.711 

90.33 

22.10 

93 

94 

91.5921.15 

91.5021.54 

,91.4022.94! 

91.31  22.34 

94 

95 

92.5721.37 

92.47!21.77 

92.3822.18! 

92.28  22.58 

95 

96 

93.5421.60 

93.44:22.00 

93.3522.41i 

93.2-5  22.82 

96 

97 

94.51  21.82 

94.42  22.23 

94.32:22.64  94.2223.06 

97 

98 

95.49  22.05 

95.39!22.46 

:95.29  22.88J 

95.19 

23.29 

9S 

99 

96.46|22.2- 

96.36 

22.69 

96.2623.11' 

96.16 

23.53 

99 

100 

97.44 

22.50 

97.34 

22.92 

97.2423.34 

97.13 

23.77 

100 

t8 

Dep 

Lat 

Dep. 

Lat. 

Dcp.|  Lat. 

Dep. 

Lat. 

^ 

3 

77  Deg 

'76|Deg. 

•76^  Deg. 

76^DegJQ 

66 


TRAVERSE  TABLE. 


g14  Deg'i 

14}1 

>eg.(114jl 

)6g'|l 

14  s  Deg.  o 

"n* 

t- 

Lat.jDep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

l!  0.971  0.24 
2   1.941  0.48! 
31  2.91   0.73 

0.97 
1.94 
2.91 

0.25!   0.97 
0.49    1.94 
0.74    2.90 

0.25 
0.50J 
0.75! 

0.97 
1.93 
2.90 

0.25 
0.51 
0.76 

i 

2 
3 

4!  3.88 

0.97 

3.88 

0.98    3.87 

1.00! 

3.87 

1.02 

4 

5 

4.85 

1.21 

4.85 

1.23    4.84 

1.25 

4.84 

1.27 

5 

6 

5.82 

1.45 

5.82 

1.48  I  5,81 

1.50! 

5.80 

1.53 

6 

7 
8 

6.79 
7.76 

1.69 

1.94 

6.78 
7.75 

1.72i  6.78 
LOT.!  7.75 

1.75; 

2,00 

6.77 
7.74 

1.78     7 
2.04!    8 

9 

8.73 

2.18| 

8.72 

2.22    8.71 

2.25 

8.70 

2.29     9 

10 

9.70 

2.42 

9.69 

2.46    9.68 

2.50 

9.67 

2.55 

10 

Ti 

10.67 

2.66 

10.66 

2.71  10.65 

2.75! 

10.64 

2.80    11 

1211.64 

2.90 

11.63 

2.95  11.62 

3.00 

11.60 

3.06   12 

13 

12.61 

3.15 

12.60 

3.20  12.59 

3.25 

12.57 

3.31    13 

1413.58  3.39 
15114.55   3.63! 

13.57 
14.54 

3.45  13.55 
3.69  14.52 

3.51 

3.76 

13.54 
14.51 

3.56!  14 

3.821  15 

16115.52  3.87 

15.51 

3.94  15.49 

4.01 

15.47 

4.07!  16 

17  16.501  4.11 

16.48 

4.18  16.46 

4.26 

16.44 

4.33    17 

18  17.47 

4.35 

17.45 

4.43  17.43 

4.51  i 

17.41 

4.58    18 

1918.44 

4.60|  18.42 

4.68  18.39 

4.76i 

18.37 

4.84    19 

20 

19.41    4.84J 

19.38 

4.92;19.36 

5.01 

19.34 

5.09  20 

21 

20.38   5.08 

20.35 

5.17  20.33   5.26 

20.31 

5.35   21 

22 

21.35   5.32 

21.32 

6.42  21.30 

5.5L 

21.28 

5.60  22 

2322.32   5.56 

22.29 

5.66  22.27 

5.76 

22.24 

5.86   23 

24'23.29   5.81 

23.26 

5.91  ,23.24 

6.01 

23.21 

6.111  24 

25:24.26 

6.05 

24.23 

6.15S24.20 

6.26 

24.18 

6.37   25 

26,25.23 

6.29125.20   6.40:25.17 

6.51 

25.14 

6.62   26 

2726.20 

6.53 

26.17 

6.65  26.14 

6.76  26.11!  6.87!  27 

2827.17 

6.77 

;27.14 

i  6.89;27.11 

i  7.01 

27.08!  7.13   28 

2928.14 

7.02 

28.11 

!  7.14  28.08 

7.26  28.04 

7.38  29 

3029.11 

7.2629.08   7.38  [29.04 

7.51 

29.01 

7.64   30, 

:_ 

1 

31 

30.08   7.50!30.05;  7.63|30.01 

i  7.76 

29.98!  7.89!  31 

3231.05   7.74 

31.02   7.88  30.98   8.01 

30.95   8.15  32 

3332.02   7.98 

31.98   8.12  31.95   8.26 

31.91   8.40   33! 

34 

32.99   8.23 

32.95   8.37 

32.92   8.51 

32.88;  8.66   34 

35 

33.96   8.47 

33.92   8.62 

33.89    8.76 

>33.85   8.911  35 

36:34.931  8.71 

34.89    8.86 

34.85   9.01 

34.81    9.  17'  36 

37'35.9Q 

8.95'35.86   9.11 

35.82 

9.26 

135.78 

9.42   37 

3836.87 

9.19 

36.83    9.35  (36.  7S 

9.51 

!36.75l  9.67 

38 

39  37.84 

9.44 

:37.8C 

>   9.6037.76   9.76 

37.71    9.93   39 

40 

38.81 

9.68 

!38.77   9.85 

38.7310.02 

;38.6810.18   40 

41 

39.78 

9.92  39.7410.09 

39.69  10.27 

39.65  10.44 

41 

42 

40.75 

10.16 

40.7110.34 

40.66  10.52 

;40.62!  10.69 

42 

43 

41.72 

10.  401  41.68  10.58 

41.63  10.77 

41.5810.95   43 

44 

42.69 

10.64 

42.65  10.83 

42.6011.02 

42.55  11.20   44 

45 

43.66 

10.89 

!43.62  11.08 

43.57  Il.27h43.52  11.46 

45 

46 

44.63 

11.13:144.5811.32 

44.5311.52 

44.4811.71 

46 

47 

45.60 

11.37 

45.55  11.57 

45.5011.77 

45.45  11.971  4 

48 

46.57 

11.61146.5211.82 

46.4712.02 

46.4212.22 

48 

4S 

47.54 

11.65  47.49  12.06 

47.44il2.27 

47.39,12.48 

49 

5C 

48.51 

12.10 

148.46  12.31 

48.41 

12.52 

48.35J12.73 

50 

•M 

Dep. 

Lat. 

Dep 

.;  Lat. 

Dep 

Lat. 

Dep.|  Lat. 

"S 

S 

70  Deg. 

75|Deg. 

752 

75*0^: 

Cfi 

TRAVERSE  TABLE. 


0 

14  Deg. 

|14±Deg.||i4iDeg. 

14£Deg. 

g 

Si.' 

Lat. 

Dep. 

Lat. 

Dep.    Lat.  Dpe. 

Lat. 

Dep. 

!» 
«•* 

51  '49.  49 

12.34 

49.43 

12.551  49.38  12.77 

49.32 

12.98 

51 

52J50.46 

12.58 

50.40 

12.80]  50.34  13.02 

50.29 

13.24 

52 

5351.43 

12.82 

51.37 

13.05J  51.31  13.27 

51.25 

13.49 

53 

5452.40 

13.06 

52.34 

13.29  52.28!  13.52 

52.22 

13.75 

54 

55153.37 

13.31 

53.31 

13.54  53.25  13.77 

53.19 

14.00 

55 

56  54.34 

13.55 

54.28 

13.78  54.22  14.02 

54.15 

14.26 

56 

57  55.31 

13.79 

55.25 

14.03  55.1814.27 

55.12 

14.51 

57 

58  56.28 

14.03 

56.22 

14.28  56.15  14.52 

56.09 

14.-77 

58 

59i57.25 

14.27 

57.18 

14.52  57.1214.77 

67.06 

15.02 

59 

6058.22 

14.52 

58.15 

14.77  58.09  15.02 

58.02 

15.28 

60 

6159.19 

14.76 

59.12 

15.02  59.06  15.27 

58.99 

15.53 

61 

6260.16 

15.00 

60.09 

15.251  60.03  15.52 

59.96 

15.79 

62 

63,61.13 

15.24 

61.06 

15.51  60.991  15.77 

60.92 

16.04 

63 

6462.10 

15.48 

62.03 

15.75  61.96:16.02 

61.89 

16.29 

64 

6563.07 

15.72 

63.00 

16.00  62.93  16.27 

62.86 

16.55 

65 

6664.04 

15.97,163.97 

16.25  63.90  16.53 

63.83 

16.80 

66 

6765.01 

16.21 

64:94 

16.49  64.87  16.78 

64.79 

17.06 

67 

68i65.98 

16.45 

65.91 

16.74  65.83  17.03 

65.76 

17.31 

68 

69  66.95 

16.69 

66.88 

16.98  66.80  17.28 

66.73 

17.57 

69 

70J67.92 

16.93 

67.85 

17.23  67.77  17.53 

67.69 

17.82 

70 

7r68.89 

17.18 

68.82 

17.48  68.74  17.78 

68.66 

18.08 

71 

7269.86 

17.42 

69.78 

17.72;'69.71  18.03 

69.63 

18.33 

72 

73  70.83 

17.66 

70.75 

17.97-J70.67  18.28 

70.59 

18.59 

73 

7471.80 

17.90 

71.72 

18.22i 

71.64  18.53 

71.56 

18.84 

74 

75:72.77 

18.14 

72.69 

18.46 

72.61  18.78 

72.53 

19.10 

75 

76 

73.74 

18.39 

73.66 

18.71 

73.68  19.03 

73.50 

19.35 

76 

77 

74.71 

18.63 

74.63 

18.95 

74.55  19.28 

74.46 

19.60 

77 

78 

75.68 

18.87l|75.60 

19.20:175.52  19.53 

75.43 

19.86 

78 

79 

76.65 

19.11 

76.57 

19.45  76.48  19.78 

76.40 

20.11 

79 

80 

77.62 

19.35 

77.54 

19.69; 

77.45  20.03 

77.36 

20.37 

80 

,  



81 

78.59 

19.60 

78.51 

19.94'  78.4220.28 

78.33 

20.62 

81 

82 

79.56 

19.84 

79.48 

20.18  79.3920.53 

79.30 

20.88 

82 

83 

80.53 

20.08 

80.45 

20.43  80.3620.78 

80.26 

21.13 

83 

84 

81.50 

20.32 

81.42 

20.681  81.32  21.03 

81.23 

21.39 

84 

85 

82.48 

20.56 

82.38 

20.92  !  82.29  21.28 

82.20 

21.64 

85 

86 

83.45 

20.81 

83.35 

21.17,83.2621.53 

83.17 

21.90 

86 

87 

84.42 

21.05 

84.32 

21.42  84.2321.78 

84.13 

22.15 

87 

88 

85.39 

21.29 

85.29 

21.66  85.2022.03 

85.10 

22.41 

88 

89 

86.36 

21.53 

86.26 

21.91!  86.17  22.28 

86.07 

22.66 

89 

90 

87.33 

21.77 

87.23 

28.151 

87.1322.53 

87.03 

22.91 

90 

91 

88.30 

22.01 

88.20 

22.40 

88.1022.78 

88.00 

23.17 

91 

92  89.27 

22.26 

89.17 

22.651 

89.07  23.04 

88.97 

23.42 

92 

93190.24 

22.50 

90.14 

22.81* 

90.0423.29 

89.94 

23.68 

93 

94 

91.21 

22.74 

91.11 

23.1-! 

91.01  23.54 

90.90 

23.93 

94 

95 

92.18 

22.98 

92.08 

23.381 

91.9723.79 

91.87 

24.19 

95 

96 

93.15 

23.22 

93.05 

23.ea 

92.94  24.04 

92.84 

24.44 

96 

97 

94.12 

23.47 

94.02 

23.88! 

93.91  24.29 

93.80 

24.70 

97 

98 

95.09 

23.71 

94.98 

24.12: 

94.8824.54 

94.77 

24.95 

98 

99 

96.06 

23.95 

95.95 

24.37 

95.8524.79 

95.74 

25.21 

99 

100 

97.03 

24.19 

96.92 

24.  62^ 

96.81  i25.04 

96.70 

25.46 

100 

•4-» 

09 

Dep. 

Lat.  j  Dep. 

Lat. 

Det.  Lat. 

Dep.i 

Lat. 

•£ 

s 

76  Deg 

|75|Deg.| 

7o£Deg. 

75£Deg. 

_4 

TRAVERSE  TABLE. 


o 

15  Deg. 

15fDeg. 

15£Deg. 

*5;Deg. 

o 

c 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

£ 

1 

0.97 

0.26 

0.96 

0.26 

0.96 

0.27 

0.96 

0,27 

~~^ 

2 

1.93 

0.52 

1.93 

0.53 

1.93 

0.53 

L92 

0.54 

2 

3 

2.90 

0.78 

2.89 

0.79 

2.89 

0.80 

2.89 

0.81 

j 

4 

3.86 

1.04 

3.86 

1.05 

3.86 

1.07 

3.85 

1.09 

i 

6 

4.83 

1.29 

4.82 

1.32 

4,82 

1.34 

4.81 

1.36 

5 

6 

5.80 

1.55 

5.79 

1.58 

5.78 

1.60 

5,77 

1.63 

6 

7 

6.76 

1.81 

6.75 

1.84 

6.75 

1.87 

6.74 

1.90 

r( 

8 

7.73 

2.07 

7.72 

2.10 

7.71 

2.14 

7.70 

2.17 

8 

9 

8.69 

2.33 

8.68 

2.37 

8.67 

2.41 

8.66 

2.44 

9 

10 

9.66 

2.59 

9.65 

2.63 

9.64 

2.67 

9.62 

2.71 

10 

11 

10.63 

2.85 

10.61 

2.89 

10.60 

2.94 

10.59 

2.99 

\ 

12 

11.59 

3.11 

11.58 

3.  IB 

11.56 

3.21 

11.55 

3.26!    2 

13 

12.56 

3.36 

12.54 

3.42 

12.53 

3.47 

12.51 

3.53 

{ 

14 

13.52 

3.62 

13.51 

3.68 

13.49 

3.74 

13.47 

3.80 

i 

15 

14.49 

3.88 

14.47 

3.95 

14.45 

4.01 

14,44 

4.07 

5 

16 

15.45 

4.14 

15.44 

4.21 

15.42 

4.28 

15.40 

4,34 

1 

17 

16.42 

4.40 

16.40 

4.47 

16.38 

4.54 

16.36 

4.61 

17 

18 

17.39 

4.66 

17.37 

4.73 

17.35 

4.81 

17.32 

4.89 

18 

19 

18.35 

4.92 

18.33 

5.00 

18.31 

5.08 

18.29 

5.16 

19 

20 

19.32 

5.18 

19.30 

5.26 

19.27 

5.34 

19.25 

5.43 

20 

21 

20.28 

5.44 

20.26 

5.52 

20.24 

5.61 

2G.21 

5.70 

2 

22 

21.25 

5.69 

2L23 

5.79 

21.20 

5.88 

21.17 

5.97 

22 

23 

22.22 

5.95 

22.19 

6.05 

22.16 

6.15 

22.14 

6.24 

23 

24 

23.18 

6.21 

23.15 

6.31 

23.13 

6.41 

23.10 

6.51 

2' 

25 

24.15 

6.47 

24.12 

6.58 

24.09 

6.68 

24.06 

6.79 

25 

26 

25.11 

6.73 

25.08 

6.84 

25.05 

6.95 

25.02 

7.06 

26 

27 

26.08 

6.99 

26.05 

7.10 

26.02 

7.22 

25.99 

7.33 

2' 

28 

27.05 

7.25 

27.01 

7.36 

26.98 

7.48 

26.95 

7.60 

28 

29 

28.01 

7.51 

27.98 

7.63 

27.95 

7.75 

27.91 

7.87 

29 

30 

28.98 

7.76 

28.94 

7.89 

28.91 

8.02 

28.87 

8.14 

30 

31 

29.94 

8.02 

29.91 

8.15 

29.87 

8.28 

29.84 

8.41 

31 

32 

30.91 

8.28 

30.87 

8.42 

30.84 

8.55 

30.80 

8.69 

32 

33 

31,88 

8.54 

31.84 

8.68 

31.80 

8.82 

31.76 

8.96 

33 

34 

32.84 

8.80 

32.80 

8.94 

32.76 

9.09 

32.72 

9.23 

34 

35 

33.81 

9.06 

33.77 

9.21 

33.73 

9.35 

33.69 

9.50 

35 

36 

34.77 

9.32 

34.73 

9.47 

34.69 

9.62 

34.65 

9.77 

36 

37 

35.74 

9.58 

35.70 

9.73 

35.65 

9.89 

35.61 

10.04 

37 

38 

36.71 

9.84 

36.66 

10.00 

36.62 

10.16 

36.57 

10.31 

38 

39 

37.67 

10.09 

37.63 

10.26 

37.58 

10.42 

37.54 

10.59 

39 

40 

38.64 

10.35 

38.59 

10.52 

38.55 

10.69 

38.50 

10.86 

40 

41 

39.60 

10.61 

39.56 

10.78 

39.5 

10.9 

39.46 

11.13 

41 

.42 

40.5" 

10.87 

!40.52 

11.05 

40.4 

11.22 

40.42 

11.40 

42 

43 

41.53 

11.13 

41.49 

11.3 

41.44 

11.49 

41.39 

11.67 

43 

44 

42.50 

11.39 

;42.45 

11.5 

42.40 

11.76 

42.35 

11.94 

44 

45 

43.47 

11.65 

43.42 

11.84 

43.36 

12.03 

43.31 

12.21 

45 

46 

44.43 

11.91 

;44.38 

12.10 

44.33 

12.29 

44.27 

12.49 

46 

47 

45.40 

12.16 

;45.35 

12.3 

45.29 

12.56 

45.24 

12.76 

47 

48 

46.3 

12.42 

146.3 

12.6 

46.25 

12.83 

46.20 

13.03 

48 

49 

47.3 

12.68 

;47.2 

12.89 

47.22 

13.09 

47.16 

13.30 

49 

50 

48.3 

12.94 

48.24 

13.1 

48.18 

13.36 

48.12 

13.57 

50 

•£ 

Dep 

Lat. 

Dep 

Lat 

Dep 

Lat 

Dep. 

Lat. 

« 

5 

75  Deg. 

1  74iDeg.74|Deg 

744Dejr 

5 

TRAVERSE  TABLE 


69 


^15  Deg. 

15£Deg.  15£Deg. 

1  52  Deg. 

0 

r 

Lat.  Dep. 

Lal.iDep.i 

Lat.  Dep. 

Lat.  Dep. 

r 

5H 

19.26!  13.20  i 

49.201  13.41  149.15  13.63 

19.0913.84 

51 

52  60.23!  13.46 

50.17  13.68  150.1113.90 

50.0514.11 

52 

5351.1913.72!  51.  13|  13.  94  51.07  14.16 

51.0114.39 

53 

5452.16  13.98:  52.10114.20  52.04  14.43 

51.9714.66 

54 

5553.13il4,24J53.06 

14.47  53.0014.70 

52.94  14.93 

55 

5654.0914.49!  54.0314.73  53.9614.97 

53.9015.20 

5i 

57  55.06  14.75 

54.99114.99  64.9315.23 

54.8615.47 

57 

58  56.02  15.01 

55.9615.26  55.8915.50 

55.8216.74 

58 

59156.99 

15.27 

56.92 

15.62:56.8515.77 

56.7816.01 

59 

60, 

>7.96  15.53  57.89 

15.78  67.8216.03 

57.75  16.29 

60 

61  58.9215.79J 

58.851  16.04  58.7816.30  58.7116.56    61 

62i59.8916.05i 

59.82 

16.31  59.751  16.57  |69.67  16.83|  62j 

63  60,85  16.31 

60.78 

16.57  60.71 

16.84 

60.63  17.10   63 

6461.82l6.56  61,75 

16.83  61.67 

17,10ti61.60!l7.37i  64 

6562.7916.82! 

62.71 

17.  10!  62.6417.37  162.56 

17.64   65 

66  63.7517.08j  63.6817.36,63.6017.64 
67  64.721  17.341  64.64  17.62  64.5617.90 

3.52 
64.48 

17.92   66 
18.191  67 

6865.68 
69  66.65 

17.60!  65.61  17.89|  66.53 
17,86'  66.5718.15  66.49 

18.17 

18.44 

65.45 
66.41 

18.46i  68 

18.73'  69 

70 

67.61 

18.12 

67.5418.41 

67.45 

18.71 

67.37 

19.00 

70 

71 

68.58 

18.38i  68.5018.68  !68.42  18.97 

68.33119.27 

71 

7269,5518.63 

69.46  18.94 

69.38  19.24 

69.3019.54 

72 

7370.5118.89 

70.43  19.20 

70.3519.51 

70.26 

19.82 

73 

74 

1.4819.15 

71.39 

,19.46 

71.31  19.78 

71.22;20.09 

74 

75 

2.44(19.41 

72.3619.73 

72.27  20.04 

72.18i20.36 

75 

76 

77 

3.4119.67 
74.38  19.93 

73.32  19.99 

74.29i20.25 

73.2420.31 

74.2020.68 

73.15 
74.11 

20.63 
20.90 

76 

77 

78 

75.3420.19 

75.2520.52 

75.16;20.84 

75.07121.17 

78 

79 

76.31 

20.45 

i76.22i20.78 

76.13121.11 

76.03121.44 

79 

80 

77,27 

20.71 

J77.18j2L04 

77.09  21.38 

77.00 

21.72 

80 

81 

78.24 

20.96 

!78Tl5!21.31 

78.05;21.65 

77.96J21.99 

81 

82 

79.21 

21.22 

79.1121.57 

79.0221.91 

78.92  22.26 

82 

83 

80.17 

21.48 

80.08  21.83 

79.98!22.18 

79.88  22.53 

83 

84 

81.14 

21.74;  81.04  22.09 

8Q.94i22.45 

80.85  22.8C 

84 

85 

82.10 

22.00 

82.0122.36 

81.9122.72 

81.81  23.07 

85 

86 

83.07 

22.26 

82.9722.62 

82.87 

22.98 

82.77  23.34 

86 

87 

84.04122.52 

83.94i22.88 

83.84 

23.25 

83.73!23.62 

87 

88 

85.0022.78 

184.90123.  15  84.8023,52 

84.70|23.89 

88 

89 

85.97  23.03 

|85.87;23.41 

85.76:23.78 

85.6624.16 

89 

90 

86.93  23.29 

86.83,23.67 

86.73 

24.05 

86.6224.43 

90 

91 

87.90 

23.55  i87.80!23.94 

87.68 

24.32 

87.58!24.7C 

< 

92 

88.87  23.81 

88.7624.20 

88.65 

24.59 

88.55l24.9- 

c 

93 

89.83  24.07  |89.73,24.46 

89.6224.85 

89.51  :25.24l  93 

94 

90.80124.33  190.69  24.72  90.5825.12 

90.47  25.5S 

c 

95 
96 

91.  76124.59  91.65  24.99  91.54;25.39j  191.43  25.  7J 
92.7324.85  92.62  25.25  !  92.51  1  25.  651  92.40  26<0( 

J 

9 

93.6925.11 

193.5825.51  93.4725.92  93.36  26.3£ 

!  i 

9 

94.66  25.36  !94.55'25.  78  94.44;26.19 

94.32i26.6C 

)    98 

9 

95.63l25.62  95.51  26.04  !95.40:26.46 

95.2826.87!  99 

1CK 

)  96.5? 

)25.8J 

lj  96.4 

8J26.30 

96.36:26.72 

1  96.25  27.14 

HOC 

S 

Dep 

.  Lat 

Dep.|  Lat. 

Dep. 

Lat. 

Dep.   Lat 

0 

5 

75  Deg 

74g  Deg. 

74^  Deg 

74i 

Deg, 

£ 

TRAVERSE  TABLE. 


Q  16  Deg.| 

rip 

)eg.;16iDes;.j 

\61D^.   J 

ri  Lat.  Dep. 

Lat.  Dep.i  Lat.  j  Dep.  I 

Lat.Dep. 

r 

1 

0.96   0.28 

0.96 

0.28;    0.961  0.28 

0.96  0.29 

i 

2   1.92  0.55 

1.92 

0.56     1.92   0.57 

1.92  0.58 

2 

Si  2.88  0.83 

2.88' 

0.84    2.88   0.85 

2.87   0.86 

S 

4|  3.85    1.10 

3.84! 

1.12    3.84|  1.14 

3.83i  1.15 

4 

51  4.81    1.38 

4.80 

1.40    4.79;  1.42 

4.79    1.44 

C 

G 

6!  5.77,  1.65!    5.76 

1.68     5.75;  1.70 

5.751  1.73 

6 

7   6.73    1.93! 

6.72 

1.96     6.71i  1.99 

6.70!  2.02 

^ 

8   7.69  2.21| 

7.68 

2.24    7.67i  2.27 

7.66i  2.31 

8 

9   8.65  2.48 

8.64 

2.62     8.63!  2.56 

8.62!  2.59     9J 

10   9.61   2.76 

9.60 

2.80    9.59!  2.84 

9.58   2.88 

10 

11  10.57   3.03 

10.56 

3.08  10.55   3.12 

10.53   3.17 

11 

1211.54  3.31  Ilr52 

3.36  11.51    3.41 

11.49   3.46 

12 

1312.50   3.58112.48 

3.64  li.46    3.69 

12.45   3.75 

13 

1413.46   3.86  113.44 

3.92  13.42   3.98 

13.41    4.03J  14 

1514.42   4.13i 

14.40 

4.20  14.33!  4.26 

14.36   4.32   15 

1615.38   4.41] 

15.36 

4.48  15.34    4.54 

15.321  4.611  16 

17116.34   4.69 

16.32 

4.76  16.30;  4.83 

16.28   4.90 

17 

1817.30   4.96! 

17.28 

6.04  17.26!  5.11 

17.24   5.19 

18 

19!  18.26   5.24! 

18.24 

5.32  18.22!  5.40 

18.19   5.48 

19 

2Q19.23   5.51 

19.20 

5.60  19.18|  5.68 

—     1 

19.15!  5.76 

20 

2120.19   5.79 

20.16 

5.88  20.14   5.96 

20.11    6.05 

21 

2221.15   6.06 

21.12 

6.16  21.09    6.26 

21.07    6JJ4;  22 

2322.11    6.34122.08 

6.44  22.05   6.63 

22.02!  6.63;  23 

2423.07!  6.62,23.04 

6.72  23.01    6.82 

22.98   6.92!  24 

2524.03   6.89J  24.00 

7.00  23.97    7.10, 

23.94J  7.20   25 

26:24.99   7.17124.96 

7.28  24.93!  7.38 

24.90;  7.49!  26 

27  25.95J  7.44 
2826.921  7.72J 

26.92 
26.88 

7.66  25.89    7.67  25.85i  7.78 
7.84  26.85    7.95  !26.8r  8.07 

27 

28 

29 

27.88   7.99, 

27.84 

8.11  27.81    8.24  27.77;  8.36J  29 

30 

28.84!  8.27 

28.80 

8.39  28.76]  8.52  |28.73i  8.65   30 

31 

32 

29.80   8.54 
30.76   8.82 

29.76 
30.72 

8.67  29.72'  8.80129.681  8.93   31 
8.95  30.68!  9.09  30.64   9.22   32 

33 

31.72   9.10 

31.68!  9.23  31.64,  9.37 

31.60   9.51    33 

34 

32.68   9.37 

32.64j  9.51  32.60!  9.66 

32.56   9.80  34 

35 

33.64  9.65 

33.60|  9.79  33.561  9.94 

33.51  10.09   35 

36 

34.61    9.92 

34.56  10.07  34.5210.22 

34.47  10.38   36 

37 

35.57  10.20 

35.5210.36  35.4810.51  '35.43  10.66   37 

38 

36.5310.47 

36.4810.63  36.44  10.79  J36.39  10.95   38 

39 

37.49  10.75 

37.44 

10.91  37.3911.08  137.35  1L24  391 

40 

38.45  11.03 

38.40 

11.19  38.3511.36 

38.30  11.53   40 

41 

39.41  11.30 

39.36 

11.47  39.3111.64 

39.2611.82   41 

42 

40.37  11.58 

40.32 

11.75  40.27!  11.  93 

40.2212.10  42 

43 

41.3311.85 

41.28il2.03  41.23|12.21 

41.1812.39   43 

44 

42.3012.13 

42.241-2.31  42.1912.50 

42.1312.68   44 

45 

43.2612.40 

43.20il2.69  43.1512.78 

43.09  12.97   45 

46 

44.2212.68 

44.16 

12.87  44.1113.06 

44.05:  13.2&  46 

47 

45.18!  12.95 

45.12 

14.15  46.06  13.35 

45.01  13.55   47 

48 

46.14113.23 

46  OS 

13.43  46.0213.  63 

45.9613.83;  48 

4947.1013.51 

47.04 

13.71  46.9813.92  146.92  14.12   49 

50 

48.06  13.78 

48.00 

13.99  47.9414.20 

47.8814.41    5Q 

tg 

Dep    Lat. 

Dep. 

Lat.  Dep.!  Lat. 

Dep.   Lat.\J 
———.2 

3 

74  De& 

73^ 

De*/.  73-  [)«£. 

*^O  i    PV               ^^^ 

/  o    L^f>tjr.  *"*^ 

TRAVERSE  TABLE. 


0 

16  Deg. 

16|Deg. 

16JDeg. 

IG^Deg. 

5 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

03 
ft- 

51 

49.02 

14.06 

48.96 

14.27 

48.90 

14.48 

48.84 

14.70 

51 

52 

49.99 

14.33 

49.92  14.55 

49.86 

14.77 

49.79 

14.99 

52 

53 

50.95 

14.61 

50.88!  14.83 

50.82 

15.05 

50.75 

15.27 

53 

54 

51.91 

14.88 

51.84il5.11 

51.78 

15.34 

51.71 

15.56 

54 

55 

52.87 

15.16 

52.80  15.39 

52.74 

15.62 

52.67 

15.85 

5b 

56 

53.83 

15.44 

53.7615.67 

53.69 

15.90 

53.62 

16.14 

56 

57 

54.79 

15.71 

54.  72i  15.95 

54.65 

16.19 

54.58 

16.43 

57 

58 

55.75 

15.99 

55.6816.23 

55.61 

16.47 

55.54 

16.72 

58 

59 

56.71 

16.26 

56.6416.51 

56.57 

16.76 

56.50 

17.00 

59 

60 

57.68 

16.54 

57.6016.79 

57.63 

17.04 

57.45 

17.29 

60 

61 

58.64 

16.81 

58.56  17.07 

58.49 

17.32 

58.41 

17.58 

61 

62 

59.60 

17.09 

59.52  17.35 

59.45 

17.61 

59.37 

17.87 

62 

63 

60.56 

17.37 

60.4817.63 

60.41 

17.89 

60.33 

18.16 

63 

64 

61.52 

17.64 

61.44  17.91 

61.36 

18.18 

61.28 

18.44 

64 

65 

62.48 

17.92 

62.4018.19 

62.32 

18.46 

62.24 

18.73 

65 

66 

63.44 

18.19 

63.36  18.47 

63.28 

18.74 

63.20 

19.02 

66 

67 

64.40 

18.47 

64.3218.75 

64.24 

19.03 

64.16 

19.31 

67 

68 

65.37 

18.74 

65.28  19.03 

65.20 

19.31 

65.11 

19.60 

68 

69 

66.33 

19.02 

66.24  19.31 

66.16 

19.GO 

66.07 

19.89 

69 

70 

67.29 

19.29 

67.20  19,59 

67.12 

19.88 

67.03 

20.17 

70 

71 

68.25 

19.57 

68.1619.87 

68.08 

20.17 

67.99 

20.46 

71 

72 

69.21 

19.85 

69.1220.15 

69.03 

20.45 

68.95 

20.75 

72 

73 

70.17 

20.12 

70.08,20.43 

69.99 

20.73 

69.90 

21.04 

73 

74 

71.13 

20.40 

7l.04i20.71 

70.95 

21.02 

70.86 

21.33 

74 

75 

72.09 

20.67 

72.00  20.99 

71.91 

21.30 

71.82 

21.61 

75 

76 

73.06 

20.95 

72.96 

21.27 

72.87 

21.59 

72.78 

31.90 

76 

77 

74.02 

21.22 

73.92 

21.55 

73.83 

21.87 

73.73 

22.19 

77 

78 

74.98 

21.50 

74.88 

21.83 

74.79 

22.15 

74.69 

22.48 

78 

79 

75.94 

21.78 

75.84 

22.11 

75.75 

22.44 

75.65 

22.77 

79 

80 

76.90 

22.05 

76.80 

22.39 

76.71 

22.72 

76.61 

23.06 

80 

81 

77.86 

22.33 

77.76 

22.67 

77.66 

23.01 

77.56 

23.34 

81 

82 

78.82 

22.60 

78.72 

22.95 

78.62 

22.29 

78.62 

23.63 

82 

83 

79.78 

22.88 

79.68 

23.23 

79.58 

23.57 

79.48 

23.92 

83 

84 

80.75 

23.15 

80.64 

23.51 

80.54 

23.86 

80.44 

24.21 

84 

85 

81.71 

23.43 

81.60 

23.79 

81.50 

24.14 

81.39 

24.50 

85 

86 

82.67 

23.70 

82.56 

24.07 

82.46 

24.43 

82.35 

24.78 

86 

87 

83.63 

23.98 

83.52 

24.35 

83.42 

24.71 

83.31 

25.07 

87 

88 
89 

84.59 
85.55 

24.26 
24.53 

84.48 
85.44 

24.62  84.38 
24.901  85.33 

24.99 

25.28 

84.27 
85.22 

25.36 
25.65 

88 
89 

90 

86.51 

24.81 

86.40 

25.18 

86.29 

25.56 

86.18 

25,94 

90 

91 

87.47 

25.08 

87.36 

25.46 

87.25 

25.85 

87.14 

26.23 

91 

92 

88.44 

25.36 

88.32 

25.74 

88.-21 

26.13 

88.10 

26.51 

92 

93 

B9.40 

25.63 

89,28 

26.02 

89.17 

26.41 

89.05 

26.80 

93 

94 

90.36 

25.91 

90.24 

26.30 

90.13 

26.70 

90.01 

27.09 

94 

95 

91.32 

26.19 

91.20 

26.58 

91.09 

26.98 

90.97 

27.38 

95 

96 

92.28 

26.46 

92.16 

26.86 

92.05 

27.27 

91.93 

27.67 

96 

97 

93.24 

26.74 

93.12 

27.14 

93.01 

27.55 

92.88 

27.95 

97 

98 

94.20 

27.01 

94.08 

27.42 

93.96  27.83 

93.84 

28.24 

98 

99 

95.16 

27.29 

95.04 

27.70 

94.9228.12 

94.80 

28.53 

99 

100 

96.13 

27.56 

96.00 

27.98 

95.88,28.40 

95.76 

28.82 

100 

•+•) 

en 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.  i  Lat. 

Dep. 

Lat. 

* 

3 

74  Deg. 

73£Deg. 

7^Deg. 

73fDe*. 

3 

TRAVERSE  TABLE. 


5 

17  Deg.    17jDeg.  IT^Deg. 

17|Deg. 

0 

s 

Lat 

Dep. 

Lat.  Dep.    Lat. 

Dep. 

Lat. 

Dep. 

en 

i 

0.96 

0.29 

0.95  0.30    0.95 

0.30 

0.95 

0.30 

1 

2 

1.91 

0.58 

1.91   0.59  i  1.91 

0.60 

1.90 

0.61 

2 

3 

2.87 

0.891 

2.87i  0.89  i  2.86 

0.90 

2.86 

0.91 

3 

4 

3.83 

1.17J 

8.82   1.19    3.81 

1.20 

3.81 

1.22 

4 

5 

4.78 

1.46 

478|  1.481    4.77 

1.50 

476 

1.52 

5 

6 

5.74 

1.75 

5.731  1.78    5.72 

1.80 

5.71 

1.83 

6 

7 

6.69 

2.05 

6.69   2.08!,  6.68 

2.10 

6.67 

2.13 

7 

8 

7.65 

2.34 

7.64   2.37 

7.63 

2.41 

7.62 

2.44 

8 

9 

8.61 

2.63 

8.60   2.67 

8.58 

2.71 

8.57 

2.74 

9 

10 

9.56 

2.92; 

9.55   2.97 

9.54 

3.01 

9.52 

3.05 

10 

11 
12 

10.52 
11.48 

3.22:  10.61  3.26 
3.51!  11.2$  3.56 

10.49 
11.44 

3.31 
3.61 

10.48 
11.43 

3.35 
3.66 

11 

12 

13 

12.43 

3.80  1  12.42   3.85 

12.40 

3.91 

12.38 

3.96 

13 

14 

13.39 

409ji  13.37!  4.15 

13.35 

4.21 

13.33 

4.27 

14 

15 

14.34 

4.39 

14.33;  4.45 

14.31 

4.51 

14.29 

4.57 

15 

16 

15.30 

468 

15.28;  4.74 

15.26 

4.81 

15.24 

4.88 

16 

17 

16.26 

4.97 

16.24:  5.04 

16.21 

5.11 

16.19 

5.18 

17 

18 

17.21 

5.26 

17.19'  5.34 

17.17 

5.41 

17.14 

5.49 

18 

19 

18.17 

5.56 

18.15;  5.63 

18.12 

5.71 

18.10 

5.79 

19 

20 

19.13 

5.85 

19.10!  5.93 

19.07 

6.01 

19.05 

6.10 

20 

21 

20.08 

6.14 

20.06!  6.23 

20.03 

6.31 

20.00 

-6.40 

21 

22 

21.04 

6.43 

21.01;  6.52 

20.98 

6.62 

20.95 

6.71 

22 

23 

21.99 

6.72 

21.971  6.82 

21.94 

6.92 

21.91 

7.01 

23 

24 

22.95 

7.02 

22.92    7.12 

22.89 

7.22 

22.86 

7.32 

24 

25 

23.91 

7.31 

23.88    7.41 

23.84 

7.52 

23.81 

7.62 

25 

26,24.86 

7.60 

24.83   7.71 

24.80 

7.82 

24.76 

7.93 

n 

27  25.82 

7.89  25.79   8.01:25.75 

8.12 

25.71 

8.23 

27 

2826.78 

8.19126.74;  8.30  26.70 

8.42 

26.67 

8.54 

58 

2927.73 

8.48 

tf?.70'  8.60J  27.66 

8.72 

27.62 

8.84 

29 

30 

28.69 

8.77 

,28.65   8.90i;28.61 

9.02 

28.57 

9.15 

30 

31 

29.65 

9.06 

29.611  9.19'  29.57 

9.32 

29.52 

9.45 

31 

32 

30.60 

9.361  130.56   9.49  30.52 

9.62 

30.48 

9.76 

33  31.56 

9.65  31.52;  9.79  31.47 

9.92 

31.43 

10.06 

33 

34|32.51 
35J33.47 

9.94  132.47  10.08  32.43 
10.23  i33.43  10.38,  33.38 

10.22 
10.52 

32.38!  10.37 
33.3310.67 

34 
35 

36;34.43 
.3735.38 

10.53  134.38  10  68  34.33 
10.82  135.34  10.97  ;  35.29 

10.83 
11.13 

34.2910.98 
35.2411.28 

36 
37 

3836.34 

11.  Ill  36.29  11.27  36.24  11.43 

36.1911.58 

Sft 

39 
40 

37.30 

38.25 

11.40 
11.69 

37.25  11.  57;  37.19  11.  73 
38.20  .11.  86!  38.15!  12.03 

37.  14l  11.  89 
38.10  12.19 

39 
40 

!                    i                     '  i                    1 

41 

42 

39.21 
40.16 

11.99|  39.16  12.16'  39.10,12.33 

12.28  140.  Ill  12.  45!  40.06!12.63 

39.05|  12.50 
40.0012.80 

4] 

4341.12 

4442.08 
4543.03 

12.57 
12.86 
13.16 

41.07,12.75  41.0lll2.93 
42.02!  13.05'  41.96  13.23 
42.98!  13.34  42.9213.53 

40.9513.11 
41.9118.41 

42.8^13.72 

43 
44 
45 

46 

43.99 

13.45 

43.93!  13.  64!  43.87  13.83 

43.81 

14.02 

47 

48 

44.95 
45.90 

13.  74  144.891  13.94 
14.03  45.841  14.23 

144.8214.13 
:45.78l  14.43 

44.76 
45.71 

14.33 
14.63 

47 

4B 

49 

46.86 

14.33 

46.801  14.53 

46.73 

14.73 

46.67 

14.94 

49 

5(J 

47.82 

14.62 

47.75ll4.83 

47.69 

15.04 

47.62 

15.24 

50, 

jn 

Dep. 

Lat. 

DepJ  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

tr? 

s 

73  Deg. 

72fDeg. 

72iDeg. 

72  1  Deg. 

Q 

TRAVERSE  TABLE. 


0 

17  Deg. 

7iDeg. 

7£Deg. 

ITJDeg. 

Q 

D 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

CO* 

>1 

8.77 

14.91 

8.71 

5.12 

8.64 

5.34 

48.57 

15.55 

51 

52 

9.73 

15.20 

9.66 

5.42 

9.59 

5.64  49.52 

15.85 

52 

53 

0.68 

15.50 

50.62 

5.72 

50.55 

5.94  50.48 

16.16 

53 

54 

1.64 

15.79 

1.57 

6.01 

1.50 

6.24  51.43 

16.46 

54 

55 

2.60 

16.08 

2.53 

6.31 

2.45 

6.54152.38 

16.77 

55 

56 

3.55 

16.37 

3.48 

6.61 

53.41 

6.84  153.33 

17.07 

56 

67 

.4.51 

16.67 

4.44 

6.90 

4.36 

7.14154.29 

17.38 

57 

58 

5.47 

16.96 

5.39 

7.20 

5.32 

7.44 

55.24 

17.68 

58 

59 

6.42 

17.25 

6.35 

7.50 

6.27 

7.74: 

56.19 

17.99 

59 

60 

7.38 

17.54 

7.30 

7.79 

7.22 

8.04; 

57.14 

18.29 

60 

61 

8.33 

7.83 

8.26 

8.09 

8.18 

8.34 

58.10 

18.60 

61 

62 

9.29 

8.13 

9.21 

8.39 

9.13 

8.64! 

59.05 

18.90 

62 

63 

jO.25 

8.42 

0.17 

8.68 

60.08 

8.94! 

60.00 

19.21 

63 

64 

1.20 

8.71 

1.12 

8,98 

1.04 

9.25; 

60.95 

19.61 

64 

65 

2.16 

9.00 

2.08 

9.28 

1.99 

9.55! 

61.91 

19.82 

65 

66 

3.12 

9.30 

3.03 

9.57 

2.96 

9.85: 

62.86 

20.12 

66 

67 

4.07 

9.59 

3.99 

9.87 

3.90 

20.15! 

63.81 

20.43 

67 

68 

5.03 

9.88 

4.94 

0.16 

64.85 

0.45 

64.76 

20.73 

68 

69 

5.99 

0.17 

5.90 

20.46 

5.81 

~0.75 

65.72 

21.04 

69 

70 

6.94 

0.47 

6.85 

0.76 

6.76 

21.05 

66.67 

21.34 

70 

71 

7.90 

0.76 

7.81 

1.05 

7.71 

21.35 

67.62 

21.65 

71 

72 

8.85 

1.05 

8.76 

1.35 

68.67 

21.65 

68.57 

21.95 

72 

73 

9.81 

21.34 

9.72 

1.65 

69.62 

21.95 

69.52 

22.26 

73 

74 

0.77 

1.64 

0.67 

1.94 

0.58 

22,25 

70.48 

22.56 

74 

75 

1.72 

21.93 

1.63 

2.24 

71.53 

22.55 

71.43  22.86 

75 

76 

2.68 

22.22 

2.58 

-2.54 

72.48 

22.85 

72.38123.  17 

76 

77 

3.64 

22.51 

3.54 

22.83 

73.44 

23.15 

73.33i23.47 

77 

78 

4.59 

22.80 

74.49 

23.13 

74.39 

23.46 

74.29i23.78 

78 

79 
80 

5.55 
6.50 

23.10 
23.39 

75.45 
76.40 

23.43 

23.72 

75.34 
76.30 

23.76 
24.06 

175.2424.08 
76.1924.39 

79 
80 

81 

77.46 

23.68 

•7.36 

24.02 

77.25 

24.36 

77.1424.69 

81 

82 

78.42 

23.97 

78.3 

24.32 

78.20 

24.66 

;78.10 

25.00 

82 

83 

79.37 

24.27 

79.27 

24.61 

79.16 

24.96!  ;79.05 

25.30 

83 

84 

80.33 

24.56 

80.22 

24.91 

80.11 

25.26!  80.00 

25.61 

84 

85 

81.29 

24.85 

81.18 

25.21 

81.07 

25.561  80.95 

25.91 

85 

86 

82.24 

25.14 

32  lc 

25.50 

82.02 

25.86!  ;81.91 

26.22 

86 

87 

83.20 

25.44 

83.*09 

25.80 

82.97 

26.16  82.86 

26.52 

87 

88 

84.15 

25.73 

84.04 

26.10 

83.93 

26.46i  83.8l|26.83 

88' 

89 

85.11 

26.02 

85.00 

26.39 

84.88 

26.76||84.76!27.13 

89 

90 

86.07 

26.31 

85.9o 

26.69 

85.83 

27.06 

85.7227.44 

90 

91 

87.02 

26.61 

86.9 

26.99 

86.79 

27.36 

86.6727.74 

91 

92 

87.98 

26.90 

87.8 

27.28 

87.74 

27.66 

87.6228.05 

92 

93 

88.94 

27.19 

88.8 

27.68 

88.70 

27.97 

88.57  28.35 

93 

94 

89.89 

27.48 

89.7 

27.87 

89.65 

28.27 

89.53  28.66 

94 

95 

90.85 

27.78 

90.7 

28.17 

90.60 

28.57 

90.48  28.96 

95 

96 

91.81 

28.0 

91.6 

28.47 

91.66 

28.87 

91.4329.2 

96 

97 

92.76 

28.3 

92.6 

28.7 

92.5 

29.17 

92.3829.5 

97 

9 
9 

93.72 
94.6 

28.6 
28.9 

93.5 
94.5 

29.0 
29.3 

93.46 
94.42 

29.47 
29.77 

93.3329.88 
94.2930.1 

28 
99 

100 

95.  6£ 

29.2 

95.5 

29.6 

95.3 

30.07 

95.2' 

130.4 

100 

:* 

Dep 

Lat 

Dep 

Lat 

Dep 

Lat. 

De7 

JLat 

ts 

/•* 

73  Deg 

72£Deg 

72iDeg. 

72iDeg 

5 

5 

TRAVERSE  TABLE. 


5 

18  Deg. 

ISfDeg. 

18±Deg. 

183  Deg,1 

d 

r 

Lat. 

Dep. 

Lat.  Dep. 

Lat.  i  Dep. 

Lat.jDep. 

a 

i 

0.95 

0.31 

0.95   0.31 

0.95!  0.32 

0.95  O.S2 

i 

2 

1.90 

0.62 

1.90   0.63 

1.90  0.63 

1.89   0.64 

2 

3 

2.85 

0.93 

2.85   0.94 

2.84  0.95 

2.84   0.96 

3 

4 

3.80 

1.24 

3.80    1.25 

3.79!  1.27 

3.79   1.29 

4 

5 

4.76 

1.55 

4.75    1.57 

4.74    1.59 

4.73   1.61 

5 

6 

5.71 

1.85 

5.70    1.88 

;  5.69,  1.90 

5.68!  1.93 

6 

7 

6.66 

2.16 

6.65   2.19 

:  6.64J  2.22 

6.63   2.25 

7 

8 

7.61 

2.47 

7.60   2.51 

i  7.59!  2.54 

7.58!  2.57 

8 

9 

8.56 

2.78 

8.55   2.82 

i  8.53  2.86 

8.52  2.89 

9 

10 

9.51 

3.09 

9.50   3.13 

1  9.48|  3.17 

9.47   3.21 

10 

11 

10.46 

3.40 

10.45  3.44 

10.43J  3.49 

10.42   3.54 

11 

12 

11.41 

3.71 

11.40   3.76 

11.38!  3.81 

11.36   3.86 

12 

13 

12.36 

4.02 

12.35   4.07 

12.33   4.12 

12.311  4.18 

13 

14 

13.31 

4.33 

13.30   4.38 

13.28'  4.44 

13.26)  4.50 

14 

15 

14.27 

4.64 

14.25   4.70 

14.22  4.76 

14.201  4.82 

15 

16 

15.22 

4.94 

15.20   5.01 

15.17   5.08 

15.15!  5.14 

16 

17 

16.17 

5.25 

16.14   5.32 

16.12!  5.39 

16.10   5.46 

17 

18 

17.12 

5.56 

17.09   5.64 

17.07J  5.71 

17.04  5.79 

18 

19 

18.07 

5.87 

18.04  5.95 

18.02'  6.03 

17.99   6.11 

19 

20 

19.02 

6.18 

18.99   6.26 

18.97;  6.35 

18.94   6.43 

20 

21 

19.97 

6.49 

19.94   6.58 

19.91    6.66 

19.89    6.75   21 

22 

20.92 

6.80 

20.89    6.89  20.86    6.98 

20.83   7.07 

22 

23 

21.87 

7.11 

21.84    7.20  21.81    7.30 

21.78    7.39 

23 

24 

22.83 

7.42 

22-79   7.52  22.76    7.62 

22.73   7.71 

24 

25 

23.78 

7.73 

23.74   7.8323,71    7.93 

23.67    8.04 

25 

26 

24.73 

8.03 

24.69    8.14  ;24.66   8.25 

24.62   8.36 

26 

27 

25.68 

8.34 

25.64   8.46  25.60   8.57 

25.57i  8.68!  27 

28 

26.63 

8.65 

26.59   8.77i  26.55    8.88 

26.51    9.00   28 

29 

27.58 

8.96 

27.54   9.08  27.50  9.20 

27.46   9.32   29 

30 

28.53 

9.27 

28.49  9.39 

!28.45;  9.52 

28.41    9.64 

30 

31 

29.48 

9.58 

29.44  9.71 

]29.40   9.84 

29.35   9.96 

31 

32 

30.43 

9.89 

30.39  10.02  30.35  10.15 

30.30  10.29 

32 

33 

31.38 

10.20 

31.34  10.33  31.29  10.47 

31.2510.61 

33 

34 

32.34 

10.51 

32.29  10.65  32.24  10.79  32.20  10,93 

34 

35 

33.29 

10.82 

33.2410.96,33.1911.11  33.1411.25 

35 

36 

34.24 

11.12 

34.1911.27  34.1411.42 

34.09  11.57 

36 

37 

35.19 

11.43 

35.14  11.  59j  35  09  11.  74 

35.04  11.89 

37 

38 

36.14 

11.74 

36.09  11.  90  J36.04  12.06 

35.98  12.21 

38 

39 

37.09 

12.05 

37.0412.21  36.98  12.37  i 

36.93  12.54 

39 

40 

38.04 

12.36 

37.99  12.53  37.93  12.69 

37.88  12.86 

40 

41 

38.99 

12.67 

38.94  12.84  38.88  13.01  'J38.82  13.18 

41 

1 

39.94 
40.90 

12.98 
13.29 

39.89,13.15  39.83  13.33  39.77  13.50 
40.84113.47:40.78  13.64  40.72  13.82 

42 

43 

4441.85 

13.60 

41.  79113.78  141.73  13.96' 

41.6614.14 

44 

45 

42.80 

13.91 

42.  7414.09;  :42.67  14.28 

42.61  14.46J  45 

46 

43.75 

14.21 

43.6914.41  143.62  14.60 

43.56  14.79 

46 

47 

44.70 

14.52 

44.  64  14.72!  !44.57  14.91 

44.5115.11 

47 

48 

45.65 

14.83 

45.5915.03 

145.52  15.23 

45.4515.43 

48 

49 
60 

46.60 
47.65 

15.14 
15.45 

46.54,15.35 
47.4815.66 

J46.47  15.55 
47.42  15.87 

46.4015.75 
47.35  16.07 

49 
50 

.^ 

Dep. 

Lat. 

Dep.!  Lat. 

Dep.  Lat. 

Dep.  Lat. 

« 

72  Deg. 

71'Deg. 

71iDeg. 

TUDe^ 

5 

TRAVERSE  TABLE. 


g 

ISDeg.  ! 

ISiDeg. 

18£Deg.| 

ISfDeg. 

o 

L. 

Lat. 

IDep. 

Lat.  Dep. 

Lat.  |  Dep. 

Lat. 

Dep. 

5148.50;15.76 

48.4315.97 

48.3616.18 

48.29 

16.39 

51 

5249.4516.07 

49.38:16.28 

49.3m6.50 

49.64 

16.71 

52 

5350.41 

16.38 

50.33'  16.60  50.2616.82 

50.19 

17.04!  63 

6451.3616.69 

51.28 

16.91 

51.21  17.13 

51.13117.36 

54 

5652.31:17.00 

52.2317.22  52.161745 

52.0817.68 

66 

6653.2617.30 

53.18 

17.54  53.11  17.77 

53.0318.00 

56 

57J54.21 

17.61 

54.1317.85  54.0518.09 

53.9818.32 

57 

68!55.  16  17.92 

55.0818.16  55.0018.40 

54,92  18.64 

58 

5956.11 

18.23 

56.0318.48  55.95118.72 

55.87 

18.96 

69 

60:57.0618.54 

56.98  18.79  56.90|  19.04 

66.82 

19.29 

60 



| 



t 

61 

58.01  18.85 

57.9319.10  57.85!  19.36 

57.76 

19.61 

61 

6258.97519.16 

58.8819.42  58.80:19.67 

58.71 

19.93 

62 

63  59.92 

19.47 

59.83 

19.73  59.74119.99 

59.66 

20.25 

63 

6460.8719.78 

60.7820.04  60.69 

20.31 

60.60 

20.57 

64 

6561.8220.09 

61.7320.36  61.64 

20.62 

61.56 

20.89 

65 

6662.7720.40 

62.68  20.67 

62.59 

20.94 

62.50 

21.22 

66 

67  63.72  20.70 

63.6320.98  63.54 

21.26 

63.44 

21.54 

67 

6864.6721.01 

64.5821.30  64.49 

21.58 

64.39 

21.86 

68 

69  65.62  21.32 

65.5321.61 

65.43 

21.89 

65.34 

22.18 

69 

70:66.5721.63 

66.48;21.92,  66.38 

22.21 

66.29 

22.50 

70 

7167.5321.94 

67.43  22.23  67.33 

22.53 

67.23 

22.82 

71 

72  68.48  22.25 

68.3822.56  68.2822.85 

68.18 

23.14 

72 

73  69.43  22.56 

69.3322.86  69.2323.16 

69.13 

23.47 

73 

7470.3822.87 

70.2823.17 

70.18 

23.48 

70.07  23.79 

74 

7571.3323.18 

71.23  23.49 

71.12 

23.80 

71.0224.11 

75 

76  72.28  23.49 

72.18 

23.80 

72.07 

24.12 

71.97 

24.431  76 

7773.2323.79 

73.13 

24.11 

73.02 

24.43 

72.91 

24.75 

77 

7874.1824.10 

74.0824.43 

73.97 

24.75 

73.8625.07 

78 

7975.1324.41 

75.03I24.74 

74.92 

25.07 

74.8125.39 

79 

8076.0824.72 

75.98|25.05 

75.87 

25.38 

75.7525.72 

80 

81  77.04  25.03 

76.93l25.37 

76.81 

25.70 

76.70l26.04   81 

82  77.99  25.34 

77.8825.68 

77.76 

26.02 

77.65 

26.36 

82 

8378.94:25.65 

78.3325,99 

78.71 

26.34 

78.60 

26.68 

83 

84  79.89:25.96 
85  80.84,26.27 

79.7726.31 
80.7226.62 

79.66 
80.61 

26.65 
26.97 

79.54 
80.49 

27.00 
27.32 

84 
85 

8681.7926.58 

81.6726.93 

81.56  27.29 

81.44 

27.64 

86 

8782.74J26.88 

82.6227.25 

82.5027.61 

82.38!27.97 

87 

8883.69127.19 

83.57  27.56 

83.45127.92 

83.33|28.29 

88 

89  84.64  27.50 

84.5227.87 

84.40 

28.24 

84.28.28.61 

89 

90i86.60J87.8JJ86.4ffe8.18 

9r86.55  28.12  86.42  28.50 
92  87.50:28.43  87.37,28.81 

85.35 

86.30 

!87.25 

28.56 

28.87 
29.19 

85.22j28.93 

86.1729.25 
87.1229.57 

90 

91 

92 

93 

88.45 

28.74 

88.32 

29.  12 

88.  J9  29.51 

88.06  29.89 

93 

9489.4029.05 

89.27;29.44 

89.1429.83 

89.01 

30.22 

94 

95  90.35!29.36i 

90.22  29.75  ,90.09 

30.14 

89.96 

30.54 

95 

96  91.30i29.67; 

91.1730.06 

191.04 

30.46 

90.91 

30.86 

96 

9792.2529.97 

92.1230.38  91.99 

30.78 

91.85 

31.18 

97 

98  93.20  30.28 
9994.1530.59 

93.07  30.69 
94.02  31.00 

92.94 
93.88 

31.10 
31.41! 

92.80 
93.75 

31.50 
31.82 

98 
S9 

100j95.11 

30.90 

94.97 

31.32 

94.83 

31.731 

94.69 

32.14100 

35 

Dep. 

Lat.i 

;  I 

Dep. 

Lat. 

Dep. 

lalj 

Dep. 

^ 

72  DegMfDeg. 

Tl^Deg.  71^Deg.,S 

TRAVERSE  TABLE. 


2 

19  Deg. 

19jDeg.  19iDeg.| 

19|Deg. 

g 

r 

Lat. 

Dep. 

Lat.  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

F 

i 

0.95 

0.33 

'0.94!  0.33 

0.94 

0.33 

0.94 

0.34 

""J 

2 

1.89 

0.65 

1.89   0.66 

1.89 

0.67 

1.88 

0.68 

S 

3 

2.84 

0.98 

2.83  0.99 

2.83 

1.00 

2.82 

1.01 

« 

4 

3.78 

1.30 

3.78    1.32 

3.77 

1.34 

3.76 

1.35 

4 

5 

4.73 

1.63 

4.72   1.65 

4.71 

1.67 

4.71 

1.69 

5 

6 

5.67 

1.95 

5.66    1.98; 

5.66 

2.00 

5.65 

2.03 

6 

7 

6.62 

2.28 

6.61 

2.31  1 

6.60 

2.34 

6.59 

2.37 

i 

8 

7.56 

2.60 

7.55 

2.64|i  7.54 

2.67 

7.53 

2.70 

8 

9 

8.61 

2.93 

8.50 

2.97!  j  8.48 

3.00 

8.47 

3.04 

9 

10 

9.46 

3.26 

9.44 

3.30!    9.43 

3.34 

9.41 

3.38J  10 

11  10.40 

3.  58* 

10.38  3.63i  10.37 

3.67 

10.35 

3.72!   11 

12  11.35 

3.91 

11.33  3.96j!11.31 

4.01 

11.29 

4.06    12 

13  12.29 

4.231 

12.27!  4.29J  12.25 

4.34 

12.24 

4.39    13 

14!  13.24 

4.56 

13.22   4.62:13.20 

4.67 

13.18 

4.73    14 

15J14.18 

4.88 

14.16   495 

14.14 

5.01 

14.12 

5.07 

15 

16,15.13 

5.21 

15.11    5.28 

15.08 

5.34 

15.06 

5.41    16 

17:16.07 

5.53!  16.05   5.60! 

16.02 

5.67 

16.00 

5.74    17 

18  17.02 

5.86  16.991  5.93 

16.97 

6.01 

16.94 

6.08 

18 

19  17.96 

6.19 

17.94   6.26 

17.91 

6.34 

17.88 

6.42 

19 

20  18.91 

6.51  18.88   6.59 

1          ' 

18.86 

6.68 

18.82 

6.76 

20 

21 

19.86 

6.84!|l9.83 

6.92 

19.80 

7.01 

19.76 

7.10 

21 

22:20.80 

7.16  20.77 

7.25 

20.74 

7.34 

20.71 

7.43 

22 

2321.75 

7.49  21.71 

7.58 

21.68 

7.68| 

21.65 

7.77 

23 

24!22.69 

7.81  22.66   7.91 

22.62 

8.01 

22.59 

8.11 

24 

25|23.64   8.14123.601  8.24 

23.57 

8.35 

23.53 

8.451  25 

26!24.58   8.46  124.55!  8.57 

24.51 

8.68 

24.47 

8.79!  26 

2725.53!  8.79  '25.49   8.90 

25.45 

9.01  25.41 

9.12|  27 

28;26.47|  9.12126.43   9.23 

26.39 

9.35  26.35 

9.46   28 

29:27.42 

9.44127.38    9.56 

27.34 

9.68|  '27.29 

9.80   29 

30^8.37 

9.77  J28.32 

9.83 

28.28 

10.01 

28.24 

10.14   30 

31  29.31 

10.09h29.27 

10.22 

29.22 

10.35 

29.18 

10.481  31 

32  30.26 
3331.20 

10.42  30.21 
10.74|]31.15 

10.55  ;30.16 
10.88  31.11 

10.68 
11.02 

30.12 
31.06 

10.81   32 
11.15  33 

3432.15 

11.07(92.10 

11.21  32.05 

11.35132.00 

11.49  34 

35  33.09 

11.39/33.04 

11.54  32.99 

11.68  132.94 

11.83  35 

36  34.04 

11.72  33.99 

11.87  J33.94 

12.02  33.88 

12.171  36 

3734.98 

12.05  34.93 

12.20  34.88 

12.35  34.82 

12.50 

37 

38  35.93 
39  36.88 

12.37  35.88 
12.70  36.82 

12.53  135.82 
12.86  '86.76 

12.68  35.76 
13.02  136.71 

12.84 
13.18 

38 
39 

40^7.82 

13.02 

37.76113.19  37.71 

13.35  37.65 

13.52 

40 

4138.77 
42  39.71 

13.35 
13.67 

38.71 
39.65 

13.52  38.65 
13.85  39.59 

13.69  38.59 
14.02i  39.53 

13.85 
14.19 

41 

(42 

4340.66 

14.00 

40.60  14.18  '40.53 

14.35  40.47 

14.53   43 

4441.60 

14.32 

41.54  14.51  41.48 

14.69  41.41 

14.87 

44 

45  42.55 

14.65 

42.48  14.84  142.42 

15.02  42.35 

15.21 

45 

46,43.49 
4744.44 

14.98 
15.30 

43.43!  15.  17  43.36 
44.37115.50  144.30 

15.36  43.29 
15.69  44.24 

15.54 

15.88 

46 
47 

48;45.38 

15.63 

45.32  15.83  45.25 

16.02  45.18 

16.22 

48 

4946.33 

15.95 

46.2616.15146.19 

16.36  46.12 

16.56 

49 

5047.28 

16.28 

47.20  16.48  |47.  13 

16.69  47.06 

16.90 

50 

*S 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

t5 

5 

71  Deg. 

70£Deg.l!70iDegJ  70]  Deg. 

3 

TRAVERSE  TABLE. 


77 


g 

19  Deg. 

19^  Deg. 

WDeg. 

1943Deg. 

2 

r 

Lat. 

Dep. 

La,. 

Dep. 

Lat;JDep. 

Lat. 

Dep. 

55* 
«-t- 

51  48.22 

16.60 

48.15 

16.81 

48.0717.02 

48.00  17.23 

51 

52 

49.17 

16.93 

49.09 

17.  14S  49.02  17.36 

48.9417.57    52 

53 

50.11 

17.26 

50.04 

17.47!  49.96il7.69 

49.8817.91    53 

54 

51.06 

17.58 

50.98 

17.80!  50.90  18.03 

50.8218.25!  54 

55 

52.00 

17.91 

51.92 

18.13  51.85  18.36 

51.76  18.59 

55 

56 

52.95 

18.23 

52.87 

18.46!  52.79  18.69 

52.71 

18.92 

56 

57 

53.89 

18.56 

53.81 

18.79;  53.73  19.03 

53.6519.26. 

57 

58 

54.84 

18.88 

54.76 

19.12 

54.67  19.36 

54.59  19.60 

58 

59 

55.79 

19.21 

55.70 

19.45  65.62  19.69 

55.53  19.94 

59 

60 

56.73 

19.53 

56.65 

19,78  1  56.56  20.03 

56.47  20.27 

60 

61 

57.68 

19.86 

57.59 

20.11 

57.5020.36 

57.41  20.61 

61 

62 

58.62 

20.19 

58.53 

20.44 

58.4420.70 

58.35  20.95 

62 

63 

59.57 

20.51 

59.48 

20.77 

59.3921.03  59.2921.29 

63 

64  60.51 

20.84 

60.42 

21.10 

60.33  21.  36  160.24  21.  63 

64 

65  61.46 

21.16 

61.37 

21.43 

61.27  21.  70 

61.1821.96 

65 

66 

62.40 

21.49 

62.31 

21.76  162.21  22.03 

62.1222.30 

66 

67 

63.35 

21.81 

63.25 

22.09 

63.1622.37 

63.06  22.64 

67 

68 

64.30 

22.14 

64,20 

22.42 

64.1022.70 

64.00;22.98 

68 

69 

65.24 

22.46 

165.14 

22.75 

65.04l23.63 

64.9423.32 

69 

70 

66.19 

22.79 

66.09 

23.08 

65.98,23.37 

65.8823.65 

70 

71 

67.13 

23.12 

67.03 

23.41 

66.9323.70 

66.8223.99 

71 

72J68.08 
7369.02 

23.44 

23.77 

67.97 

68.92 

23.74 
24.07 

67.8724.03 
68.81  24.37 

67.7624.33 
68.7124.67 

72 
73 

74,69.97 

24.09 

69.86 

24.40 

69.7624.70 

69.6525.01 

74 

75170.91 
76  71.86 

24.42 
24.74 

70.81 
71.75 

24.73 
25.06 

70.7025.04 
71.6425.37 

70.59  25.34 
71.5325.68 

75 
76 

77 

72.80 

25.07 

72.69 

25.39 

72.58  25.70 

72.47  26.02 

77 

78 

73.75 

25.39 

73.64 

25.72 

73.53  26.04 

73.41  26.36 

78 

79 

74.70 

25.72 

74.58 

26.05 

74.47  26.37 

74.35  26.70 

79 

80 

75.64 

26.05 

75.53 

26.38 

75.4l9.fi  70 

7A.9-Q  07.03 

80 

81 

76.59 

26.37 

76.47 

26.70 

76.3527.04 

76.24 

27.37 

81 

82 

77.53 

26.70 

77.42 

27.03 

77.30  27.37 

77.18 

27.71 

82 

83 
84 

78.48  27.02 
79.42  27.35 

78.36 
79.30 

27.38 
27.69 

78.2427.71 
79.1828.04 

78.12 
79.06 

28.05 
28.39 

83 

84 

85  80.37  27.67 

80.25 

28.02 

80.1228.37 

80.00i28.72 

85 

86j81.31  28.00 

81.19 

28.35 

81.07  28.71  !i80.94  29.06 

86 

8782.2628.32 

82.14 

28.68 

82.01  29.04  81.8&2Q.4Q 

87 

88  83.21 
8984.15 
9085.10 

28.65 
28.98 
29.30 

;83.08 
84.02 
'84.97 

29.01 
29.34 
29.67 

82.95  29.37,  82.82J29.74 
83.9029.71  83.7630.07 
84.84  30.04  |84.  71  30.41 

88 
89 
90 

91  86.04 

29.63 

85.91 

30.00 

85.7830.38  85.65'30.75 

91 

92  86.99  29.95 

86.86 

30.33'  !86.  72  30.71  -86.59 

31.09 

9S 

93,87.9330.28 

87.80 

30.66,  87.6731.04  '87.5331.43 

9J 

9488.88130.60 

88.74 

30.99JI88.61  31.381  88.4731.76 

94 

95189.82 

30.93 

89.69 

31.32  89.5531.71 

89.4132.10 

95 

9690.77 
97  91.72 

31.25  |90.63 
31.58  91.58 

31.651  90.49  32.05 
31.98|l91.  44  32.38 

90.35  32.44 
191.2932.78 

96 
97 

98 
99 

92.66 
93.61 

31.91 

32.23 

92.52 
93.46 

32.31  |92.38  32.71  1  '92.24  33.  12 
32.64:93.3233.05  93.1833.45 

98 
99 

100 

94.55 

32.56 

94.41 

32.97  94.26  33.38 

94.1233.79 

100 

•M 

.22 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.  Lat. 

Dep. 

Lat. 

-*j 

W) 

71  Deg. 

702  Deg. 

70jDeg. 

70  1  Deg. 

•  .—< 

78 


TRAVERSE  TABLE. 


g;20Deg.20$De«. 

2QJ  Deg.  20£Deg.  M 

^ 

?-  Lat.lDep. 

Lat.|Dep. 

Lat. 

Dep.i  Lat. 

Dep.   * 

1    0.94  0.34 

'  0.94   0.35 

0.94 

0.35    0.94 

0.35     1 

2    1.88;  0.68 

1.88]  0.69 

1.87 

0.701  1.87 

0.71     2 

3   2.82    1.03 

1  2.81!  1.04 

2.81 

1.05    2.81 

1.06     3 

4  3.76j  1.37 

!  3.75!  1.38 

3.75 

1.40    3.74 

1.42     4 

5   4.70!  1.71 

|  4.69!  1.73 

4.68 

1.75    4.68 

1.77     5 

6   5.64   2.05 

i  5.63;  2.0ft 

5.62 

2.10    5.61 

2.13     6 

7   6.58   2.39 

|  6.57    2.42 

6.56 

2.45    6.55 

2.48     7 

8   7.52  2.74 

7.51    2.77 

7.49 

2.80    7.48 

2.83     8 

9    8.46   3.08 

8.44   3.12 

8.43 

3.15    8.42 

3.19     9 

10   9.40i  3.42 

1  9.38   3.46 

9.37 

3.50    9.35 

3.54   10 

11  10.34   3.76 

10.32   3.81 

10.30 

3.85  10.29 

3.90  ll 

1211.28   4.10 

11.26    4.15 

11.24 

4.20  11.22 

4.25    12 

1312.22   4.46 

12.20!  4.50 

12.18 

4.55  12.16 

4.61    13 

1413.16   4.79 

13.13!  4.85 

13.11 

4.90  13.09 

4.96    14 

1514.10   5.13 

14.07J  5.19 

14.05 

5.25  14.03 

5.31    15 

1615.04   5.47 
1715.97    5.81 

15.011  5.54 
!  15.95!  5.88 

14.99 
15.92 

5.60  14.96 
5.95  15.90 

5.67    J6 
6.02    17 

1816.91    6.16 

I16.89J  6.23 

16.86 

6.30  16.83 

6.38    18 

1917.85    6.50 

17.83   6.58 

17.80 

6.65  17.77 

6.73    19 

2018.79;  6.84 

118.76   6.92 

| 

18.73 

7.00  18.70 

7.09   20 

21  19.73    7.18 

Il9.70!  7.27 

19.67 

7.36  19.64 

7.44   21 

2220.67    7.52 

20.64    7.61 

20.61 

7.70  20.57 

7.79   22 

2321.61    7.87 

21.58    7.96 

21.54 

8.05  2K61 

8.15   23 

2422.55    8.21 

22.52    8.31 

22.48 

8.40  22.44 

8.50   24 

2523.49   8.55 

23.45    8.65 

23.42 

8.76  23.38 

8.86   25 

2624.43   8.89 

24.39    9.00 

24.35 

,9.11  24.31 

9.21    26 

2725.37    9.23 

25.33   9.35 

25.29 

9.46  25.25 

9.57   27 

2826.31,  9.58 

26.27    9.69 

28.23 

9.81  26.18 

9.92   28 

2927.25i  9.92 

27.21  10.04 

27.16 

10.16  27.12 

10.27   29 

3026.1010.06 

9ft  is!  10.38 

28.10 

10.51  28.05 

10.63  30 

3129.1310.60 

29.0810.73 

29.04 

10.86  28.99 

10.98   31 

32  30.07  10.94 

30.02  11.08 

29.97 

11.21  29.92 

11.34   32 

3331.01  11.29 

30.96  11.42 

30.91 

11.56  30.86 

11.69   33 

3431.95  11.63 

31.9011.77 

31.85 

11.91  31.79 

12.05   34 

3532.8911.97 

32.8412.11 

32.78 

12.26  32.73 

12.40  35 

36  33.83  12.31 

33.77'  12.46 

33.72 

12.61  33.66 

12.75   36 

3734.7712.65 

34.71:12.81 

34.66 

12.96  34.60 

13.11   37 

3835.71  13.00 

35,6513.15 

35.59 

13.31  35.54 

13.46   38 

39  36.65  13.34 

36.591  13.50 

36.63 

13.66  S«.47 

13.82   39 

4037.5913.68 

37.53  13.84 

37.4? 

14.01  37.41 

14.17    40 

41  38.53  14.02 

38.47;  14.  li- 

38.40 

14.36  38.34 

14.53    41 

42  39.47  14.36 

39.40:  14.54 

39.34 

14.71  39.28 

14.88   42 

43  40.41  14.71 

40.34  14.8h 

40.28 

15.06  40.21 

15.23   43 

4441.3515.05 

41.2815.23 

41.21 

15.41  41.15 

15.59   44 

45  42.29  15.39 

42.22:15.58 

42.  15 

15.76  42.08 

15.94  45 

4643.2315.73 

42.1615.92 

43.09 

16.11  43.02 

16.30   46 

4744.1716.07 

44.09il6.2-/ 

44.02 

16.46  43.95 

16.65   47 

4845.1116.42 

45.0316.61 

44.S6 

16.81  44.89 

17.01    48 

49  46.04  16.76 

45.9716.96 

17.16  45.82 

17.36   49 

5046.9817.10 

46.9117.31 

46.83 

17.51  46.76 

17.71    50 

^j  Dep.  Lat. 

Dep.l  Lai. 

Dep. 

Lat.|  Dep. 

Lat.  +1 

l  co 

P   70  Deg. 

69|Deg. 

69iDeg.|69{Deg.S 

TRAVERSE  TABLE. 


o 

20  Deg. 

20*Deg. 

201  Deg. 

20peg. 

9 

f 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.  Dep. 

r 

51 

47.92 

17.44 

47.8517.65 

47.77 

17.86 

47.6918.07   61 

62 

48.86 

17.79 

48.7918.00 

48.71  18.21 

48.6318.42   62 

53 

49.80 

18.13 

49.72  18.34 

49.64ll8.56 

49.5618.78   53 

54 

50.74 

18.47 

50.6618.69 

50.58 

18.91 

50.50!  19.  13,  64 

55 

51.68 

18.81 

51.60  19.04 

51.52 

19.26  151.43'  19.49    55 

56 

52.62 

19.15 

52.5419.38 

52.45 

19.61 

152.37  19.84;  66 

57 

53.56 

19.50 

53.4819.73 

53.39 

19.9.6 

53.30120.19)  67 

58 

54.50 

19.84 

54.42  20.07 

54.33 

20.31 

54.2420.55    58 

59 

55.44 

20.18 

55.35  20.42 

55.26 

20.66 

55.  17120.90!  59 

60 

56.38 

20.52 

56.2920.77 

56.20 

21.01 

56.lll21.26 

_]. 

60 

61 

57.32 

20.86 

57.2321.11 

57.1421.36 

57.0421.61 

61 

62 

58.26 

21.21 

58.1721.46 

58.0" 

21.71 

57.98:21.97 

62 

63 

59.20 

21.55 

59.ir21.81 

59.0122.06 

58.9122.32 

63 

64 

60.14 

21.89 

60.0422.15 

59.9522.41 

59.85|22.67j  64 

65 

61.08 

22.23 

60.98  22.50 

60.8822.76 

60.7823.03   65 

66 

62.02 

22.57 

61.9222.84 

61.8223.11 

61.7223.381  66 

67 

62.96 

22.92 

62.8623.19 

62.7623.46 

62.6523.74 

67 

68 

63.90 

23.26 

63.8023.54 

63.69  23.81 

63.59;24.09 

68 

69 

64.84 

23.60 

64.74-23.88 

64.6324.16 

64.5224.45!  69 

70 

65.78 

23.94 

65.67|24.23 

65.57  24.51 

,65.4624.80 

70 

71 

66.72 

24.28 

66.61  24.57 

66.5024.86 

66.3925.15 

71 

72 

67.66 

24.63 

67.55^24.92 

67.44  25.21 

67.3325.51 

72 

73 

68.60 

24.97 

68.49 

25.27 

68.38 

25.57 

68.2625.86    73 

74 

69.54 

25.31 

69.43i25.61 

69.31  25.92 

69.2026.22    74 

75 

70.48 

25.65 

70.3625.96 

70,2526.27 

70.1426.57    75 

76 

71.42 

25.99 

7L30  26.30 

71.1926.62 

71.0726.93i  76 

77 

72.36 

26.34 

72.24J26.65 

72.1226.97 

72.0127.28   77 

78 

73.30 

26.68 

73.1827.00 

73,0627.32 

72,9427.631  78 

79 

74.24 

27.02 

74.12:27.34 

74.0027.67 

73.  88  27.991  79 

80 

75.18 

27.36 

75.06 

27.69 

74.9328.02 

I7481|28.34 

80 

81 

82 

76.12 
77.05 

27.70 
28.05 

75.99 
76.93 

28.04 

28.38 

76*81  28^72 

75.7528.70   81 
76.6829.05   82 

83 

77.99 

28.39 

77.87:28.73 

77.7429.07 

77.6229.41    83 

84 

78.93 

28.73 

78.81:29.07 

78.6829.42 

78.55l29.76 

84 

85 

79.87 

29.07 

79.7529.42 

79.6229.77 

79.4930.11 

85 

86 

80.81 

29.4l||80.68:29.77 

80.5530.12 

!  80.42  30.  47 

86 

87 

81.75 

29.76jl81.62i30.11 

81.49  30.47 

81.3630.82   87 

88 
89 

82.69 
83.63 

30.10 
30.44 

82.5630.46 
83.50,30.80 

82.4330.82 
83.3631.17 

82.2931.18   88 
83.2331.53j  89 

90 

84.57 

30.78 

84.4431.15 

84.3031.52 

84.1631.89   90 

91 

85.51 

31.12 

85.38'31.50 

85:2431.87 

85.1032.24   91 

92 

86.45 

31.47 

86.3131.84 

86.1732.22 

86.0332.59   92 

93 

87.39 

31.81 

87.2532.19 

87.1132.57 

86.9732.95]  93 

94 

88.33 

32.151 

88.19;32.54 

88.05  32.92 

87.9033.30!  94 

95 

89.27 

32.491 

89.1332.88 

88.98  33.271  88.84  33.66!  95 

96 

90.21 

32.83 

90.0733.23 

89.9233.62 

89.77  34.01!  96 

97 

91.15 

33.18 

91.0033.57 

90.8633.97 

90.71  34.37)  97 

98 

92.09 

33.52 

91.94'33.92 

91.7934.32 

91.6434.72   98 

99 

93.03 

33.86 

92.88'34.27 

92.7334.67 

92.58|35.07    99 

100 

93.97 

34.20 

!!i2 

34.61 

93.6735.02 

93.5135.43100 

t5 

Dep. 

Lat. 

|Dep. 

"L^ 

Dep. 

Lat. 

Dep.   Lat. 

+1 

Q 

70  Deg. 

69iDeg. 

691  Deg. 

5 

TRAVERSE  TABLE. 


S 

21  Deg.  21^Deg. 

21£Deg.j 

21iM- 

)eg. 

2 

r 

Lat. 

Dep.    Lat. 

Dep. 

Lat. 

Dep. 

Lat.  <Dep. 

55" 

'e-t- 

1 

0.93 

0.36    0.93 

0.36 

0.93 

0.37 

0.93i 

0.37 

1 

2 

L87 

0.72ll  1.86 

0.72 

1.86 

0.73 

1.86 

0.74 

2 

3 

2.80 

1.08,1  2.80 

1.09* 

2.79 

1.10   -2.79J 

1.11 

3 

4 

3.73 

1.43U  3.73 

1.45 

3.72 

1.47!!  3.72J 

1.48 

4 

5 

4.67 

1.79  !  4.66 

1.81 

4.65 

1.83;    4.64; 

1.85 

5 

6 

5.60 

2.15 

5.59 

2.17 

5.58 

2.20 

5.571 

2.22 

6 

7 

6.54 

2.51 

6.52 

2.54 

6.51 

2.57 

6.50! 

2.59 

7 

8 

7.47 

2.87 

7.46 

2.90 

7.44 

2.93 

7.43, 

2.96 

8 

9' 

8.40 

3.23 

8.39 

3.26 

8.37 

3.30 

8.36: 

3.34 

9 

9.34 

3.58 

9.32 

3.62 

9.30 

3.67 

9.29 

3.71 

10 

11 

10.27 

3.94 

10.25 

3.99 

10.23  1  4.03 

10.221 

4.08 

11 

12 

11.20 

4.30 

11.18 

4.35 

11.17 

4.40 

11.15 

4.45    12 

13 

12.14 

4.66 

12.12 

4.71 

12.10 

4.76 

12.07 

4.82   13 

14 

13.07 

5.02 

13.05 

5.07 

13.03j  5.13 

13.00, 

5.19    14 

15  14.00 

5.38 

13.98 

5.44 

13.96!  5.50 

13.93 

5.56!  15 

16  14.94 

5.73 

14.91 

5.80 

14.89 

5.86 

14.86 

5.931  16 

17  15.87 

6.09 

15.841  6.16 

15.82 

6.23 

15.79 

6.30!  17 

18  16.80 

6.45 

16.78 

6.52 

16.75 

6.60 

16.72 

6.67    18 

19  17.74  6.81 

17.71 

6.89 

17.68 

6.96 

17.65 

7.04   19 

2018.67 

7.17 

18,64 

7.25 

18.61 

7.33 

18.58 

7.41  1  20 

21 

19.61 

7.53 

19.57 

7.61 

19.54 

7.70 

19.50 

7.78   21 

2220.54 

7.88 

20.50 

7.97 

20.47 

8.0R 

20.43 

8.15   22 

23121.47 

8.24 

21.44 

8.34 

21.40 

8.43 

21.36 

8.521  23 

2422.41 

8.60 

22.37 

8.70 

22.33 

8.80 

22.29 

8.89:  24 

25  23.34 

8.96 

23.30 

9.06 

23.26 

9.16 

23.22 

9.26   25 

26124.27 

9.32 

24.23 

9.42 

24.19 

9.53 

24.15 

9.63 

26 

27 

25.21 

9,68 

26,16 

9.79 

25.12 

9.90 

25.0810.01    27 

28 

26.1410.03 

26.1010.15 

26.05!  10.26 

26.01 

10.38   28 

2927.0710.39 

27.0310.51 

26.98  10.63 

26.94 

10.751  29 

30 

28.01 

10.75 

127.96  10.87 

27.91 

11.00 

27.8611.12   30 

31 

28.9411.11 

28.8911.24 

28.8411.36 

28.79  11.49!  31 

32  29.87 
3330.81 

11.47 
11.83 

29.8211.60 
30.7611.96 

29.77  11.73 
30.70  12.09 

29.72  11.86:  32 
30.65il2.23!  33 

3431.7412.18 
3532.6812.54 

31.6912.32 
32.6212.69 

31.63!  12.46 
32.5612.83 

31.58 
32.51 

12.60   34 
12.9?!  35 

36133.61 

12.90 

33.5513.05 

33.50 

13.19 

33.44 

13.34   36 

37 

34.54 

13.26 

34.4813.41 

34.43 

13.56 

34.37 

13.71    37 

38 

35.4813.62 

35.42 

13.77: 

35.36  13.93 

35.29 

14.08   38 

39 

36.41 

13.98 

'36.35  14.  14  (36.29  14.29 

36.22  14.45;  39 

40 

37.3414.33 

37.2814.50 

1  |  i 

37.2214.66 

37.15 

14.82:  40 

41 

38.28  14.69 

138.21  14.86 

38.1515.03 

38.0815.19   4] 

42 

39.21 

15.05 

39.1415.22 

39.0815.39 

39.01 

15.56   42 

43 

40.14 

15.41 

'40.08  15.58 

40.01 

15.76 

39.9415.93:  43 

44 

41.08  15.77 

141.01 

15.95 

40.9416.13 

40.87l6.301  44 

45 

42.01  16.  13  141.94;  16.31 

41.87 

16.49 

41.8016.68   45 

46 

42.94 

16.48!  S42.87  16.67 

42.8016.86 

42.7317.05   46 

47J43.881  16.84  43.80,17.03 

43.73  17.23 

43.65  17.421  47 

48  44.81  17.20  44.74,17.40  44.66  17.59 
49  45.75  17.56il45.6717.76  |45.59il7.96 

44.58 
45.51 

17.78 
18.16 

48 
49 

50 

46.68 

17.92  46.6018.12 

! 

46.52  18.33 

46.44  18.53 

50 

+Z 

Dep. 

Lat.iJDep. 

|  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

ts 

s 

69 

DegJ!68|Deg. 

eSJDeg. 

eSJDeg. 

£ 

TRAVERSE  TABLE. 


8i 


3-   Lat.  Dep. 

Lat.:Dep.  j  Lat.  Dep. 

••    -  .  .      _.»••-.-  - 

Lat.  Dep. 

i 

51  47.61  18.28 
5248.5518.64 

!47.53  18.48  47.45  18.69lJ47.37  18.90 
48.46  18.85  48.38  19.06ii48.30  19.27 

51 

52 

5349.4818.99 

49.40  19.21  49.31  19.42 

49.23  19.64 

53 

54  50.41  19.35 

50.33  19.57  50.24  19.79 

50.1620.01 

54 

5651.35  19.71'  51.26  19.93  51.1720.16  151.08  20.38 
56  52.28  20.071  52.  19  20.30  52.10  20.52  J62.01  20.75 

55 

57  53.21  20.43 

53.1220.66  53.0320.89 

52.9421.12 

57 

£854.15:20.  79 

54.06  21.02  53.96  21.26jJ53.87  21.49   58 

5955.08121.14 

54.9921.38  64.89  21.62)  54.80  21.861  59 

60  56.01  21.50 

55.9221.75  56.8321.99 

55.7322.23 

60 

61  56.9521.86 

56T8522.il  56.76^2.36(156.6622.60 

61 

62  57.88l22.22 
63  58.82  22.58 

57.7822.47  67.6922.72 
58.7222.83  58.6223.09 

57.59  22.97 
58.5223.35 

62 
63 

64  59.75'22.94 

59.65  23.20  59.55  23.46 

59.44  23.72 

64 

65  60.68  23.29 

60.5823.56  60.4823.82 

60.37  24.09 

65 

6661.6223.65  61.5123.92  61.4124.19 

1,61.3024.46   66 

67  62.55  24.01 

62.44  24.28  62.34  24.56 

!62.23  24.83   67 

68  63.48  24.37  63.38  24.65  63.27  24.92 

63.  1625.20!  68 

6964.4224.73  64.3125.01  64.2025.29 

64.0925.57    69 

7065.3525.09  65.2426.37  65.1325.66 

65.0225.94   70 

"T!  66.28  25.44  66.17  25.73  66.06  26.021:65.95  26.31    71 

7267.2225.80  67.1026.10  66.9926.39 

166.87  26.681  72 

73  68.15  26.16  68.0426.46  J67.9226.76 

'67.8027.05 

73 

7469.0826.52  68.9726.82 

68.8527.12 

68.7327.42 

74 

7570.0226.88  69.9027.18 

69.7827.49 

69.6627.79    75 

76  70.95  27.24  70.83  27.55 

70.7127.85 

70.6928.16    76 

7771.8927.59  71.76  i7.91 

71.6428.22 

171.5228.53   77 

7872.8227.95  72.7028.27 

72.57  28.591  S72.45  28.90   78 

7973.7528.31  73.63  28.6S 

73.5028.95 

73.38  29.27 

79 

80  74.69  28.67  74.56  29.00 

74.43  29.32:  74.30  29.64 

89 

i           _ 

_  ______ 

_____  _____ 

!       _ 



81  75.62  29.03  75.49  29.36 

75.36  29.69 

75.2330.02 

81 

8276.5529.39  76.4229.72 

76.29  30.05 

176.1630.3S 

82 

8377.4929.74  77.3630.08 

77.2230.42 

77.0930.76 

83 

8478.4230.10  78.2930.44 

78.lb3C.79 

78.0231.13    84 

8579.3530.46  79.2230.81 

79.09  31.15'|78.95<51.50    85 

8680.2930.82  80.  15  31.  17 

80.02  31.52 

79.88  31.81: 

86 

8781.2231.18  81.0831.53  80.9531.89 

80.81  32.24 

I  87 

8882.1631.54  82.0231.89  181.68  32.25,181.74  32,61 

88 

89  83,09  31.85 

)  82.9532.26 

82.81  32.62 

82.66  32.9S 

89 

9084.0232.26  83.8832.62 

83.74  32.99  183.59  33.3i 

>   90 



__        _ 

i  

9184.9632.61  84.8132.98 

84.67  33.351  84.52  33.72   91 

9285.8932.97  85.7433.34 

86.6033.72  !  86.45  34.0S 

92 

9386.8233.33  86.6833.71 
9487.7633.69  87.6134.07 

86.53  34.08  86.38  34.46!  93 
87.4634.45  87.31  34.83i  94 

9588.6934.04  88.5434.43 

88.3934.82  88.24  35.20i  95 

9689.6234.40  89.4734.79 

89.3235.18!  89.1735.57   96 

97  90.56  34.76  90.40  36.16 

90.2535.55 

190.0936.94   97 

9891.4935.12  91.34  35.5i 

91,18  35.92 

91.0236.31    98 

99  92.42  35.48  92.27  35.88 

92.1136.28!:91.9536.69i  99 

100  93.36  35.84  93.20  36.24 

93.0436.65 

•|92.88  37.06]  100 

+1  Dep.!  Lat.  Dep.  Lat. 

Dep.  Lat. 

JDep.  Lat.  „_; 

,JS  .  

-j  .         

-i    . 

... 

.3 

w  69  Deg.  6&|Deg. 

68£Deg. 

68;Deg.Q 

16 


•as 


TRAVERSE  TABLE. 


S 

r 

22  Deg.  |22iDeg.  22iDeg. 

22fDeg. 

5 

00* 

Lat. 

Dep. 

Lat.  Dep. 

Lat.jDep. 

Lat. 

Dep. 

i 

0.93 

0.37 

0.93   0.38 

0.92 

0.38 

0.92 

0.39 

1 

2 

1.85 

0.76 

1.85   O.V6J    1.85 

0.77 

1.84 

0.77 

8 

3 

2.78 

1.12 

2.78    1.14 

i  2.77 

1.15 

2.77 

1.16 

8 

4 

S.71 

1.60 

3.70    1.51 

3.70    1.53 

3.69 

1.55 

4 

5 

4.64 

1.87 

4.63    1.89 

4.62    1.91 

4.61 

1.93 

5 

6 

5.56 

2.25;  |  5.55   2.27 

5.54!  2.30 

5.53 

2.32 

6 

7 

6.49 

2.62 

6.48   2.65 

6.47 

2.68 

6.46 

2.71 

8 

7.42 

3.00 

7.40   3.03 

7.39 

3.06 

7.38 

3.09 

9 

8.34 

3.37 

8.33   3.41 

8.31 

3.44 

8.30 

3.48 

9 

10 

9.27 

3.75 

9.26   3.79 

1  9.24 

3.83 

9.22 

3.87 

10; 

11 

10.20 

4.12"l0.18   4.17 

10.16 

4.21 

10.14 

4.25 

n 

12 

11.13 

4.50  ill.ll    4.54 

11.091  4.59 

11.07 

4.64 

12 

13 

12.05 

4.87  12.08   4.92 

12.01 

4.97 

11.99 

5.03 

13 

14 

12.98 

5.2412.96    6.30 

12.93 

5.36 

12.91 

5.41 

15 

13.91 

5.62  13.68   5.68 

13.86 

5.74 

13.83 

5.60 

15 

16 

14.83 

5.99114.81    6.06 

14.78 

6.12 

14.76 

6.19 

16 

17 

15.76 

6.37  15.73    6.44 

15.71 

6.51 

15.68 

6.57 

17 

18 

16.69 

6.74  16.66    6.82 

16.63!  6.89 

16.60 

6.96 

18' 

19 

17.62 

7.1217.59    7.19 

17.65 

7.27 

17.62 

7.35 

19 

20 

18.54 

7.49!  18.51    7.57 

18.48 

7.65 

18.44 

7.73 

20 

21 

19.47 

7.87  19.44'  7.95 

19.40 

8.04  19.37 

8.12 

21 

2220.40 

8.24 

20.36!  8.33 

20.33 

8.42  20.29    8.51 

22 

2321.33 

8.62 

21.29J  8.71 

21.25 

8.80  21.2li  8.89 

23 

2422.25 
25I23.18 

8.99 
9.37 

22.211  9.09 
23.14!  9.47 

22.17 
23.10 

9.18  22.13   9.28 
9.57123.05   9.67 

24 
25 

2624.11 

9.74 

24.06    9.84  24.02 

9.95i  23.98  10.05 

26 

27 

25.03  10.11,  24.99  10.22  24.94  10.33,  24.90  10.44 

27 

og 

25.9610.49  25.9210.60  25.8710.72;  25.82  10.83 

28' 

2926.89ilO.86  26.8410.98  26.79  11.  10i  26.74  11.21 

29 

30 

27.8211.24 

27.77  11.36  27.72 

11.48 

27.67  11.60 

30 

31 

28.74J11.61 

28.69  11.74  28.64 

11.86 

128.5911.99 

31 

32 
33 

29.6711.99  99.6212.12  29.5612.25 
30.60;  12.36!  30.54  12.50  30.49!  12.63 

29.51  12.37 
30.4312.76 

32 
33 

34 

31.52jl2.74  31.47  12.87  31.41 

13.01  31.35  13.15 

S4 

35 

32.4,513.11  32.3913.25  32.34  13.39  32.28  13.53 

35 

3633.38  13.49  33.32  13.63  33.2613.78  33.20  13.92 

36 

37134.31  13.86  34.24  14.01  34.18  14.16  34.12  14.31 

37 

38J35.23  14.24  35.1714.39  36.11 

14.54!  35.04  14.70 

38 

39j36.16  14.61  36.10  14.77  36.0314.92i  35.97!l5.08 

39 

40J37.0914.98j  37.02  16.15  36.96,  16.31j  36,89  15.47 

•11  38.01  15^36  37.95  15^52  37.88ll5.69  37.81J15.86 
42  38.94:  15.  73i  38.87  15.90  38.80  16.071  38.73  16.24 

40 

41 

42 

4339.87 
4440.80 

16.11  39.8016.28  39.7316.46  i39.  65  16.63 
16.48  40.72  16.66  40.65  16.84  !40.  58  17.02 

43 
44 

45  41.72 
46/J2.65 

16.86J  41.65  17.04  41.57  17.22 
17.23  42.57  17.42i  42.6017.60 

141.5017.40 
142.42  17.79 

45 
46 

47  43.58  17.61  43.50  17.80!  i43.42i  17.99 

i43.34  18.  18 

47 

48 
49 

44.50 
45.43 

17.98  44.43  18.18,  '44.3518.37 
18.36  145.35  18.55i  45.27|18.75 

i44.27l8.56 
45.19  18.95 

4B 
4(9 

60 

46.36 

18.73 

146.28  ,18.98]  46.19 

19.13 

J46.ll 

19.34 

50 

OS 

Dep. 

Lat, 

DepJ  Lat. 

Dep. 

Lat. 

[Dep. 

Lat. 

ti 

s 

68  Deg. 

67fDeg. 

67^: 

Deg. 

J67iDeg.jS 

TflAVERSE  TABLE. 


022  Deg. 

22£  Deg. 

22  J  Deg. 

22|Deg. 

g 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

£ 

51147.29 

19.10 

47.20 

19.31 

47.12 

19.52 

47.03 

19.72 

51 

52  48.21 

19.48 

48.13 

19.69 

48.04 

19.90 

47.95 

20.11 

52 

5349.14 

19.85 

49.05 

20.07 

48.97  20.28 

48.88 

20.50 

53; 

54:50.07 

20.23 

49.98 

20.45 

49.89 

20.66 

49.80 

20.88 

54 

5551.00 

20.60 

50.90 

20.83 

50.81 

21.05 

50.72 

21.27 

55 

5651.92 

20.98 

51.83 

21.20 

51.74.21.43 

51.64 

21.66 

56 

5752.85 

21.35 

52.76 

21.58 

52.66i21.81 

52.57 

22.04 

67 

5853.78 

21.73 

53.68 

21.96 

53.5922.20 

53.49 

22.43 

5* 

59  64.70 

22.10 

54.61 

22.34 

54.5122.58 

54.41 

22.82 

59 

6055.63 

22.48 

55.53 

22.72 

55.43 

22.96 

55.33 

23.20 

60 

6156.56 

22.85 

56.47 

23.10 

56.36^23.34 

56.25 

23.59 

61 

62  57.49 

23.23 

57.38 

23.48 

57.28J23.73 

57.18 

23.98 

62 

63  58.4] 

23.60' 

58.31 

23.85 

58.2024.11 

58.10 

24.36 

63 

64  59.34 

23.97 

59.23 

24.23 

59.1324.49 

59.02 

24.75 

64 

6560.27 

24.35 

60.16 

2-4.61 

60.05  24.87 

59.94 

25.14 

65 

6661.19 

24.72 

61.09 

24.99 

60.98  25.26 

60.87 

25.52 

66 

6762.12 

25.10 

62.01 

25.37 

61.90  25.64 

61.79 

25.91 

67 

68  63.05 

25.47 

62.94 

25.75 

62.82  26.02 

62.71 

26.30 

68 

69  63.98 

25.85 

63.86 

26.13 

63.75  26.41 

63.63 

26.68 

60 

7064.90 

26.22 

64.79 

26.61 

64.67  26.79 

64.55 

27.07 

70 

7165.8S 

26.60 

6a.71 

26.88 

65.6027.17 

65.48 

27.46 

71 

7266.76 

26.97 

66.64 

27.26 

66.5227.55 

66.40 

27.84 

72 

73  67.68 

27.35 

67.56 

27.64 

67.44  27.94 

67.32 

28.23 

73 

74  68.61 

27.72 

68.49 

28.02 

68.37  28.32 

68.24 

28.62 

74 

7569.54 

28.10 

69.42 

28.40 

69.2928.70 

69.17 

29.00 

75 

7670.47 

28.47 

70.34 

28.78 

70.21  29.08 

70.09 

29.39 

76 

7771.39 

28.84 

71.27 

29.16 

71.1429.47 

71.01 

29.78 

77 

7872.32 

29.22 

72.19 

29.53 

72.06  29.85 

71.93 

30.16 

78 

7973.25 

29.59 

73.12 

29.91 

72.99  30.23 

72.85 

30.55 

79 

80 

74.17 

29.97 

74.04 

30.29 

73.91  30.61 

73.78 

30.94 

80 

81 

75.10 

30.34 

74.97 

30.67 

74.83  31.00 

74.70 

31.32 

81 

82 

76.03 

30.72 

75.89 

31.05 

75.76:31.38 

75.62 

31.71 

82 

83 

76.96 

31.09 

76.82 

31.43 

76.68iSl.76 

76.54 

32.10 

83 

84 

77.88 

31.47 

77.76 

31.81 

77.61132.15 

77.46 

32.48 

s4 

85 

78.81 

31.84 

78.67 

32.19 

78.5332.53 

78.39 

32.87 

85 

86 

79.74 

32.22 

79.60 

32.56 

79.4532.91 

79.31 

33.26 

86 

87 

80.66 

32.59 

80.52 

32.94 

80.3833.29 

80.23 

33.64 

87 

88 

81.59 

32.97 

81.45 

33.32 

81.30^3.68 

81.15 

34.03 

8S 

89 

82.52 

33.34 

82.37 

33.70 

82.23:34.06 

82.08 

34.42 

89 

90 

83.45 

33.71 

83.30 

34.08 

83.16:34.44 

83.00 

34.80 

90 

91 

84.37 

34.09 

84.22 

34.46 

84.07!34.82 

83.92 

35.19 

91 

92 

85.30 

34.46 

85.15 

34.84 

85.00*35.21 

84.84 

35.58 

92 

93 

86.23 

34.84 

86.08 

35.21 

66.92^35.59 

85.76 

35.96 

93 

9487.16 

35.21 

87.00 

35.59 

86.84  35.97 

86.69 

36.35 

94 

95  88.08 

35.5'J 

87.93 

35.97 

87.77  36.35 

87.61 

36.74 

95 

96  89.01 

35.96 

88.85 

36.35 

88.69  36.74 

88.53 

37.12 

96 

97189.94 

36.34 

89.78 

36.73 

89.6237.12 

89.45 

37.51 

97 

98 

90.86 

36.71 

90.70 

37.11 

90.5437.50 

90.38 

37.90 

98 

99 

91.79 

37.09 

91.63 

37.49 

91.4637.89 

91.30 

38.28 

99 

100 

92.72 

37.46 

92.55 

37.86 

92.39  38.27 

92.22 

38.67 

100 

« 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

^ 

5 

68  Deg. 

67£Deg. 

67iDeg. 

67^De^. 

TRAVERSE  TABLE. 


g23  Deg. 

23£Deg.i  23£19eg.  23|Deg. 

^ 

f*   Lat.  Dep. 

Lat.  Dep.    Lat.  Dep. 

Lat.lDep. 

r 

1    0.92   0.39 

0.92  0.39;    0.92   0.40 

0.92 

0.40 

~1 

2    1.84   0.78 

1.84   0.79!    1.83!  0.80 

1.83 

0.81 

2 

31  2.76    1.17 

2.761  1-18    2.75!  1.20 

2.75 

1.21 

8 

4;  3.68    1.56 

3.68!  1.68     3.67:  1.59 

3.66 

1.61 

i 

5    4.60   1.95!  4.59|  1.97     4.59    1.99 

4.58!  2.01 

5 

6    5.52    2.34  '  5.51    2.37     5.50;  2.39 

5.49 

2.42 

6 

7    6.44   2.74     6.43   2.76     6.42i  2.79 

6.41 

2.82 

• 

8j  7.36  3.13 

7.35,  3.16     7.34   3.19 

7.32 

3.22 

8 

9    8.28   3.52 

8.27!  3.55    8.25   3.59 

8.24 

3.62 

9 

10    9.20   3.91! 

9.19'  3.95    9.17i  3.99 

9.15 

4.03 

10 

1  t__r_           ( 

^^            1  _  _                                      i 

11  10.13   4.30 

10.11    4.34  10.091  4.39 

10.07 

4.43 

11 

12  11.05   4.69 

11.03|  4.74  ll.OOi  4.78^ 

10.98 

4.83 

12 

13  11.97    5.081 

11.94!  5.13  11.92'  5.18i 

11.90 

6.24 

lf 

1412.89    5.47J 

12.86!  5.53   12.84    5.58 

12.81 

5.64 

14 

15  13.81    5.86J 

13.78    5.92  13.76    5.98 

13.73 

6.04   15 

16  14.73    6.25 

14.70    6.32  14.67    6.38 

14.64!  6.44 

16 

17  15.65    6.64 

15.62    6.71  15.59    6.78 

15.56 

6.85 

17 

18  16.57    7.03J 

16.54    7.11  16.51    7.18 

16.48 

7.25 

18 

19  17.49    7.42! 

17.46    7.50  17.42    7.58 

17.39    7.65 

19 

2018.41    7.811 

18.38    7.89  18.34    7.97 

18.31 

8.05 

20 

—  —  _  ____ 

-  1      •  .                              j 

___ 

—  —  —    . 

21  19.33    8.21 

19.29   8.29  19.26    8.37! 

19.22 

8.46   21 

2220.25    8.60 

20.21    8.68  20.18    8.77! 

20.14 

8.86   22 

2321.17    8.99 

21.13   9.08  21.09    9.17 

21.05 

9.26   23 

2422.09    9.38 

22.05   9.47  22.01  '  9.57 

21.97 

9.67   24 

2523.01    9.77 

22.97   9.87  22.93   9.97 

22.8810.07   25 

26  23.93  10.  16  23.89  10.26  23.84  10.37 

23.8010.47   26 

2724.85  10.55  24.81  10.66  24.7610.77 

24.71 

10.87!  27 

2825.77  10.94  i25.73  11.06  25.68  11.16 

26.6311.28   28 

2926.69  11.33 

26.64  11.45  26.59  11.66 

26.5411.68   29 

30  27.62  11.72 

27.5611.84  27.51  11.96 

27.4612.08 

30 

31  28.54  12.11 

28.48  12.24  28.43  12.36 

28.37 

12.49J  SI 

32  29.46  12.50 

29.40  12.63  29.35  12.76 

29.29 

12.89   32 

3330.3812.89 

30.32  13.03  S0.26  13.16! 

30.21 

13.29   33 

34  31.30  13.28s 

31.2413.42  31.1813.56! 

31.1213.69i  34 

35  32.22  13.68  32.16  13.82  32.10  13.96  132.04  14.10'  35 

36  33.14  14.07  ,33.08  14.21  33.01  14.35 
37  34.06  14.46  84.00  14.61  33.93  14.75 

32.95  14.50i  36 
33.8714.90   37 

38  34.98  14.85; 

34.91  15.00  34.85  15.15! 

34.7815.30  38 

39  35.90  15:24 
40  36.82  15.63 

35.8316.39  35.77:15.56 
36.75  16.79|36.68|  15.951 

35.7015.71    39 
36.6116.11    4Q 

4137.7416.02 

37.67  16.18  37.60  16.35i 

37.5316.51    41 

42  38.66  16.4F 

38.59  16.58  38.52;16.75 

38.4416.92   42 

43  39.58  16.80 

39.51  16.97  39,4317.15 

39.3617,32   43 

4440.5017.19 

40.43  17.37  40.35  17.54  40.2717.72!  44 

45  41.42  17.58 

41.35  17.76  41.27!  17.94  J41.  1918.12   45 

46i42.34  17.97 

42.26  18.16  42.1818.34 

42.1018.53  46 

47  43.26  18.36 

43.1818.65  43.1018.74 

43.02 

18.93  47 

4844.1818.76 

44.1018.95  44.0219.14 

43.93  19.33j  48 

4945.1019.15 

45,02  19.34  44.94  19.54 

44.8519.73   49 

60  46.03  19.54 

45.9419.74  45.85J  19.94 

45.77.20.14j  50 

^J   Dep.   Lat. 

CO 

Dep.J  Lat.  Dep.  i  Lat. 

Dep. 

Lat. 

ts 

Sj  67  Deg. 

66|Deg.|66|Deg.! 

66i  Deg.  A: 

TRAVERSE  TABLE. 


^23  Deg. 

23tDeg. 

23|Deg. 

23|Deg.|  Q 

r  Lat. 

Dep. 

Lat.Dep. 

Lat.JDep.  ! 

Lat.  Dep. 

r 

5146.95 

19.93 

46.86'20.13 

46.77!20.34i'46.68l20.54~5l 

52  47.87  20.52 

47.7820.53 

47.69!20.73: 

47.6020.94    52 

5348.7920.71 

48.70  20.92  '48.60  21.  13 

48.5121.35    53 

5449.7121.10 

49.61  21.32  '49.52  21.53 

49.4321.75    54 

5550.6321.49 

50.53  21.71IJ50.44  21.93 

50.3422.15   55 

5651.5521.88 

51.45  22.11(151.36  22.33 

51  .2622.55J  56 

57  52.47122.27  52.37  22.50'  52.27  22.73 
58  53.39  22.66  153.29  22.90  53.19  23.13 

52.1722.96   57 
53.0923.36    58 

5954.3123.05 

54.21  23.29;  154.  11  23.53 

54.0023.76   59 

60  55.23!23.44 

55.1323.68  55.0223.92 

54.9224.16 

60 

6156.15 

23.83 

56.05  24.08!|55.S4!24.32 

56,8324.57    61 

62  57.07 

24.23 

56.97i24.47!!56.8624.72 

56.75  24.97 

62 

63  57.99 

24.62 

57.88  24.87!'57.  77  25.12 

57.6625.37 

63 

64  58.91  25.01 

58.80;25.26  58.69  25.52 

58.68  25.78 

64 

6559.83,25.40 

59.7225.66,159.6125.92 

59.5026.18 

65 

66  60.75  25.79 

60.  64  26.05,  160.53  26.32 

60.4126.58   66 

6761.6726.18 

61.56  26.45:i61.44  26.72 

61.3326.98   67 

68  62.59(26.57 

62.48  26.84  '62.36  27.  11 

62.2427.39   68 

69  63.51  26.96 

63.40  27.24;  '63.28  27.51 

63.1627.79 

69 

70  64.44  27.35 

64.32  27.63:64.  19  '27.91 

64.0728.19 

70 

|  

1 

1 

7165.36 

27.74 

65.2328.03  65.1128.31 

64.9928.59 

71 

72  66.28 

28.13 

66.1528.42  66.0328.71 

65.90  29.00 

72 

7367.20 

28.52J!67.07  28.82:;66.95  29.11 

66.82  29.40 

73 

7468.12 

28.911  67.99  29.2ll!67.86  29.51 

67.7329.80 

74 

7569.04 

29.30  68.91  29.61;  68.78  29.91 

68.6530.21 

75 

76  69.96 

29.70 

69.83  30.00  69.70  30.30 

69.5630.61 

76 

77,70.88 

30.09 

70.75  30.40!  70.61  30.70 

70.4831.01 

77 

7871.80 

30.48 

71.6730.79  71.5331.10 

,71.3931.41 

78 

7972.72 
80  73.64 

30.87 
31.26 

72.5831.18:72.4531.50 
73.5031.58  73.3631.90 

72.31  31.82 
73.2232.22 

79 
80 

___  —  — 

, 

—  —  —  — 

' 

[           —  — 

— 

81  74.56 

31.65 

74.4231.97 

74.28  32.30 

74.1432.62 

81 

82  75.48 

32.04 

75.3432.37 

75.20  32.70 

75.0633.03 

82 

83  76.40 

32.43 

76.26  32.76 

76.1233.10 

75.97  33.43 

83 

8477.32 

32.82 

77.1833.16 

77.03  33.49 

76.8933.83 

84 

85  78.24 

33.21 

78.1033.55 

77.9533.89 

77.8034.23 

85 

86179:16 

33.60 

79.02  33.95 

78.87  34.29 

78.7234.64 

86 

87  80.08  33.99 

79.9334.34 

79.78i34.69 

79.63!35.04 

87 

8881.00 

34.38 

80.85  34.74 

80.7035.09 

:80.55  35.44 

88 

89  81.92 

34.78 

81.7735.13 

81.6235.49 

81.4635.84 

89 

90  82.85J35.17 

82.6935.53 

82.5435.89  82.3836.25 

'           I 

90 

9183.7735.56 

83.61  35.92 

83.4536.29 

83.2936.65 

91 

9284.6935.95 

84.53  36.32 

84.3736.68 

84.21  37.05 

92 

93  85.61  36.34 

85.4536.71 

85.2937.08 

85.1237.46 

93 

9486.5336.73 

86.3737.11 

86.2037.48 

86.04;37.86 

94 

9587.4537.12 

87.29  37.50 

87.12-37.88 

86.9538.26 

95 

96  88.37  37.51 

88.20  37.90 

88.04  38.28 

87.8738.66 

96 

97  89.29(37.90 

89.1238.29!'88.9538.68 

!88.  79|39.07 

97 

98  90.21 

38.29 

90,04  38.68  !39.  87  39.08 

89.7039.47 

98 

9991.13 

38.68 

190.96  39.08!  90.79  39.  48 

90.62iS9.87 

99 

100  92.0S 

39.07 

91.8839.47 

91.7139.87 

91.5340.27 

100 

i 

«  Dep 

Lat. 

Dep.  Lat. 

Dep.  Lat. 

Dep.l  Lat. 

0  67  Deg. 

66|Deg. 

66  J  Deg. 

GG^Deg. 

17 


TRAVERSE  TABLE, 


5 

24  Deg. 

24£Deg 

24£Deg 

24-jDeg 

& 

33 

La 

Dep. 

La 

Dep 

La 

Dep 

La 

Dep 

o 

0.9 

0.41 

0.9 

0.4 

0.9 

0.4 

0.9 

0,4 

$ 

1.8, 

0.81 

1.8 

0.8 

1.8 

0.8 

1.8 

0.84 

< 

2.7 

1.22 

2.7 

1.2 

2.7 

1.2 

2.7 

1.26 

,1 

3.6 

1.63 

3.6, 

1.6 

3.6 

1.6 

3.62 

1.6 

£ 

4.5 

2.03 

4.5 

2.0 

4.5 

2.0 

4.5 

2.0 

€ 

5.4 

2.44 

5.4 

2.4 

5.4 

2.4 

5.4 

2.5 

6.3 

2.85 

6.3 

2.8 

6.3 

2.9 

6.3 

2.9 

8 

7.3 

3.25 

7.2 

3.2 

7.2 

3.3 

7.2 

s.5 

t 

8.2 

3.66 

8.2 

3.7 

8.1 

3.7 

8.1 

3.7 

10 

9.1 

4.07 

9.1 

4.1 

9.1 

4.1 

9.0 

4.1 

1 

11 

10.0 

4.47 

10.0 

4.5 

10.0 

4.5 

9.9 

4.6 

12 

10.9 

4.88 

10.9 

4.9 

10.9 

4.9 

10.9 

5.0 

13 

11.8 

5.29 

11.8 

5.3 

11.8 

5.3 

11.8 

5.44 

12.7 

5.69 

12.7 

5.75 

12.7 

5.8 

12.7 

5.8 

15 

13.7 

6.10 

13.6 

6.16 

13.6 

6.22 

13.6 

6.2 

16 

14.6 

6.51 

14.5 

6.57 

14.5 

6.64 

14.5 

6.7 

17 

15.5 

6.92 

15.50 

6.98 

15.4 

7.05 

15.4 

7.1 

18 

16.44 

7.32 

16.4 

7.39 

16.3 

7.46 

16.3 

7.5 

19 

17.3 

7.73 

17.3 

7.80 

17.2 

7.88 

17.2 

7.9 

20 

18.2 

8.13 

18.2 

8.21 

18.2 

8.29 

18.1 

8.3 

2( 

21 

19.1 

8.54 

19.1 

8.63 

19.1 

8.71 

19.0 

8.7 

21 

22 

20.1 

8.95 

20.0 

9.04 

20.0 

9.12 

19.98 

9.2 

22 

23 

21.0 

9.35 

20.9 

9.45 

20.93 

9.54 

20.89 

9.63 

23 

24 

21.93 

9.76 

21.8 

9.86 

21.84 

9.95 

21.80 

10.05 

24 

25 

22.84 

10.17 

22.7 

10.2 

22.75 

10.37 

22.70 

10.47 

25 

26 

23.75 

10.58 

23.7 

10.68 

23.6 

10.78 

23.6 

10.89 

26 

27 

24.67 

10.98' 

24.6 

11.09 

24.57 

11.20 

24.52 

11.30 

27 

28 

5.58 

1.39! 

25.5o 

11.50 

25.48 

11.61 

25.43 

1.72 

28 

29 

26.49 

1.80' 

26.4 

11.91 

26.39 

2.03 

26.34 

2.14 

29 

30 

7.41 

2.20| 

27.35 

12.32 

27.30 

2.44 

27.24 

2.66 

30 

[ 

31 

8.32 

2.61 

28.26 

2.73 

28.21 

2.86 

28.15 

2.98 

31 

32 

29.23 

3.02 

29.18 

3.14 

29.12 

3.27 

29.06 

3.40 

32 

3330.15 
3431.06 

3.42 
3.83 

30.09 
31.00 

3.55 
3.96 

30.03 
30.94 

3.68 
4.10 

29.97 
30.88 

3.82 
4.23 

33 
34 

3531.97 

4.24 

31.91 

4.38 

31.85 

4.51 

31.78 

4.65 

35 

36 

32.89 

4.64 

32.82 

4.79 

32.76 

4.93 

32.69 

5.07 

36 

37 

33.80 

5.05 

33.74 

6.20 

33.67 

5.34 

33.60 

5.49 

37 

38 

34.71 

5.46 

34.65 

5.61 

34.58 

5.76 

34.51 

5.91 

38 

39 

35.63 

5.86 

35.56 

6.02 

35.49 

6.17 

5.42 

6.33 

39 

40 

36.54 

6.27 

36.47 

6.43 

36.40 

6.59 

6.33 

6.75 

40 

41 

57.46 

6.68 

37.38 

6.84 

7.31 

7.00 

7.23 

7.16 

41 

42 

J8.37 

7.08  i 

38.2i 

7.25 

8.22 

7.42 

8.14 

7.58 

42 

43 

39.28 

7.49  | 

39.21 

7.66 

9.13 

7.83 

9.05 

8.00 

43 

44 

H).20 

7.90  | 

40.12 

8.07 

0.04 

8.25 

9.96 

8.42 

44 

45 

11.11 

8.30  i 

41.03 

8.48 

0.95 

8.66 

0.87 

8.84 

45' 

46 

12.02 

8.71  | 

41.94 

8.89 

1.86 

9.08j 

1.77 

9.26 

46 

47 

12.94 

9.12i 

42.85 

9.30 

42.77 

9.49 

2.68 

9.68 

47 

48 

13.85 

9.52' 

13.76 

9.71 

43.68 

9.91 

43.59 

0.10 

48 

49 

M.76 

9.93 

44.68 

0.13 

4.59 

0.32 

44.50 

0.51 

49 

50 

15.68 

0.34  ' 

45.59 

0.54 

5.50 

0.73 

5.41 

0.93 

50 

3 

Dep. 

Lat. 

Dep. 

Lat. 

ep. 

Lat. 

ep. 

Lat. 

<J 

Q 

5 

56  Deg. 

35|Deg. 

5£Deg.| 

5|Deg. 

5 

TRAVERSE  TABLE. 


i 

24  Deg. 

24£Deg. 

24iDeg. 

4^Deg. 

5 

* 

Lat. 

Dep. 

Lat.lDep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

51 

46.59 

0.74 

46.5020.95 

46.41 

1.15 

46.32 

1.35 

51 

52 

47.50 

1.15 

47.4121.36 

47.32 

1.56 

7.22 

1.77 

52 

53 

48.42 

1.56 

48.3221.77 

48.23 

1.98 

8.13 

2.19 

53 

54 

49.33 

1.96 

49.24i22,18 

49.14 

2.39 

9.04 

2.61 

54 

55 

50.24 

2.37 

50.15:22.59 

50.05 

.2.81 

49.95 

3.03 

55 

56 

51.16 

2.78 

51.06  23.00 

50.96 

23.22 

50.86 

23.44 

56 

57 

52.07 

23.18 

51.97,23.41 

51.87 

22.64 

51.76 

23.86 

57 

58 

52.99 

23.59 

52.88;23.82 

52.78 

24.05 

52.67 

24.28 

68 

59 

53.90 

24.00 

53.7924.23 

53.69 

24.47 

53.58 

24.70 

59 

60 

54.81 

24.40 

54.71  !24.64 

54.60 

24.88 

54.49 

25.12 

60 

61 

55.73 

24.81 

55.6225.05 

55.51 

25.30 

55.40 

25.54 

61 

62 

56.64 

25.22 

56.53  25.46 

56.42 

25.71 

56.30 

25.96 

62 

63 

57.55 

25.62 

57.4425.88 

57.33 

26.13 

57.21 

26.38 

63 

64 

58.47 

26.03 

58.35  26.29 

58.24 

26.54 

58.12 

26,79 

64 

65 

59.38 

26.44 

59.2626.70 

59.15 

26.96 

59.03 

27.21 

65 

66 

60.29 

26.84 

60.18!27.11 

60.06 

27.37 

59.94 

27.63 

66 

67 

61.21 

27.25 

61.0927.52 

60.97 

27.78 

60.85 

28.05 

67 

68 

62.12 

27.66 

62.00'27.93 

61.88 

28.20 

61.75 

28.47 

68 

69 

63.03 

28.06 

62.9128.34 

62.79 

28.61 

62.66 

28.89 

69 

70 

63.95 

28.47 

63.8228.75 

63.70 

29.03 

63.57 

29.31 

70 

71 

64.86 

28.88 

64.74!29.16 

64.61 

29.44 

64.48 

29.72 

71 

72 

65.78 

29.28 

65.6529,57 

65.52 

29.86 

65.39 

30.14 

72 

73 

66.69 

29.69 

66.5629.98 

66.43 

30.27 

66.29 

30.56 

73 

74 

67.60 

30.10 

67.4730.39 

67.34 

30.69 

67.20 

30.98 

74 

75 

68.52 

30.51 

68.38  30.80 

68.25 

31.10 

68.11 

31.40 

75 

76 

69.43 

30.91 

69.29 

31.21 

69.16 

31.52 

69.02 

31.82 

76 

77 

70.34 

31.32 

70.21 

31.63 

70.07 

31.93 

69.93 

32.24 

77 

78 

71.26 

31.73 

71.12 

32.04 

70.98 

32.3o 

70.84 

32.66 

78 

79 

72.17 

32.13 

72.03 

32.45 

71.89 

32.76 

71.74 

33.07 

79 

80 

73.08 

32.54 

72.94 

32.86 

72.80 

33.18 

72.65 

33.49 

80 

81 

74.00 

32.95 

73.85 

33.27 

73.71 

33.59 

73.56 

33.91 

81 

82 

74.91 

33.35 

74.76 

33.68 

74.62 

34.00 

74.47 

34.33 

82 

83 

75.82 

33.76 

75.68 

34.09 

75.53 

34.42 

75.38 

34.75 

83 

84 

76.74 

34.17 

76.59 

34.50 

76.44 

34.83 

76.28 

35.17 

84 

85 

77.65 

34.57 

77.50 

34.91 

77.35 

35.25 

77.19 

35.59 

85 

86 

78.56 

34.98 

78.41 

36.32 

78.26 

35.66 

78.10 

36.00J  86 

87 

79.48 

35.39 

79.32 

35.73 

79.17 

36.08 

79.0 

36.42   87 

88 

80.39 

35.79 

80.24 

36.14 

80.08 

36.49 

79.92 

36.84|  88 

89 

81.31 

36.20 

81.15 

36.55 

80.99 

36.9 

80.8" 

37.26|  89 

90 

82.22 

36.61 

82.06 

36.96 

81.90 

37.3 

81.73 

37.68 

E 

9 

63.13 

37.0 

!82.97 

37.38 

82.8 

37.7 

82.6 

38.10 

92 

84.05 

37.42 

;83.88 

37.79 

83.72 

38.1 

83.5 

38.52!  92 

93 

84.96 

37.83 

84.79 

38.20 

84.63 

38.5 

84.46 

38.94i  93 

94185.87 

38.23 

|85.71 

38.61 

85.5438.9 

85.37 

39.35 

94 

95|86.79 

38.64 

;86.62 

39.02 

86.4539.40 

86.27 

39.77 

95 

9687.70 

39.05 

!87.53 

39.43 

87.3639.8 

87.18 

40.19 

96 

97  88.6 

39.45 

88.44 

39.84 

88.27140.2 

88.08 

40.61 

97 

98  89.53 

39.8 

89.35 

40.25 

89.1840.6 

89.0C 

41.09 

98 

99i  90.44 

40.2 

90.26 

40.66 

90.09  41.0 

89.91 

41.45 

99 

IOC 

91.3S 

40.6 

91.18 

41.07 

91.00 

41.4 

90.81 

41.87 

100 

tf 

Dep 

Lat 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

Lat. 

•si 

3 

66  Deg 

65£l)eg. 

|65JDeg 

6MD?   . 

TRAVERSE  TABLE, 


c 

25  Deg.  ^b\ 

Deg. 

,25jDeg. 

253Ueg.!0 

So* 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.  j  Dep. 

,  Lat.|Dep.   ~ 

i 

0.91 

0.42 

0.90 

0.43 

1  0.90  0.43 

0.90!  0.43     1 

2 

1.81 

0.85 

1.81 

0.85 

l.Sli  0.86 

1.80 

0.87|    2 

3 

2.72 

1.27 

2.71 

1.28 

i  2.71    1.29 

2.70 

1.30     3 

4 

3.63 

1.69 

3.62 

1.71 

i  3.611  1.72 

3.60 

1.74;       4 

5 

4.53 

2.11 

4.52 

2.13 

4.51 

;  2.15 

4.50 

2.17     5 

6 

5.44 

2.54 

5.43 

2.56 

5.42;  2.58 

5.40 

2.61     ft 

7 

6.34 

2.96 

6.33 

2.99 

6.32   3.01 

6.30 

3.04;     7 

8 

7.25 

3.38 

7.24 

3.41 

7.22;  3.44 

7.21 

3.48!    & 

9 

8.16 

3.80 

8.14 

3.84 

1  8.12 

3.87 

8.11 

3.91 

i    9 

10 

9.06 

4.23 

9.04 

4.27 

j  9.03  4.31 

9.01 

4.34   10 

111  9.97 

4.65 

9.95 

4.69 

9.93  4.74    9.91 

4.781  11 

12!  10.88 

5.07 

10.85 

5.12 

10.83 

!  5.17 

10.81 

5.21 

1  n 

13'll.78 

5.49  11.76 

6.55 

11.73 

5.60 

11.71 

5.65 

13 

1412.69 

5.92  12.66 

5.97 

12.64 

6.03 

12.61 

6.08    14 

15!13.59|  6.34 

13.57 

6.40 

13.54 

6.46 

13.51 

6.52 

15 

1614.50 

6.76 

14.47 

6.83 

14.44 

6.89 

14.41 

6.96 

16 

17  15.41 

7.18 

15.38 

7.25 

15.34 

7.32 

15.31 

7.39 

17 

1816.31 

7.61  16.28 

7.68 

16.25 

7.75 

16.21 

7.82 

18 

19  17.22 

8.03!  17.  18 

8.10 

17.15 

8.18 

17.1li 

8.25 

19 

2018.13 

8.45 

18.09 

8.53 

18.05 

8.61 

18.'01 

8.69 

20 

21  19.03 

8.87 

18.99 

8.96 

18.95 

9.04! 

1891; 

9.12 

21 

22;  19.94 
2320.85 

9.30i  19.90 
9.7220.80 

9.38;  19.86 
9.8120.76 

9.471 
9.90 

19!S2' 

20.72 

9.56 
9.99 

22 
23 

2421.75 

10.  14  '21.71 

10.24 

21.66  10.33 

21.62  10.43 

24 

25!22.66  10.57lj22.61 

10.66 

22.56  10.76 

22.52  10.86 

25 

26  23.56  10.99  23.52  11.09 

23.4711.19 

23.42 

11.30 

26 

2724.4711.41:24.4211.52 

24.37  11.62 

24.32  11.73 

27 

28  25.38  11.83i  25.32  11.94 

25.27  12.05 

25.2212.16 

28 

29'26.28  12.26i  26.23  12.37' 

26.1712.48 

26.12  12.60 

29 

3027.19jl2.68jl27.1312.80 

27.0812.92 

27.0213.03 

30 

31 

28.10 

13.10  28.04  13.22  27.98  13.35 

27.92  13.47 

31 

32  29.00 

13.52  28.94  13.65 

29.88  13.78 

28.82  13.90 

32 

3329.91  13.95  29.85  14.08  29.79  14.21 
34'30.8l!  14.37  I30.75  14.  50!  30,69  14.64 

29.72  14.34 
30.62  14.77 

33 
34 

35'31.72 

14.79;  !31.  66  14.93 

31.59  15.07 

31.52  15.21 

35 

3632.63 

15.21  ;32.56  15.36 

32.49  15.50 

32.43  15.64 

36 

37133.53 

15.64  33.46 

15.78 

33.4015.93 

33.33  16.07 

37 

3834.44 

16.06  34.37  16.21 

34.301  16.36 

34.23 

16.51 

38 

39|35.35 

16.48  35.27  16.64 

35.20!16.79 

35.13  16.94 

39 

40  36.25 

16.90;  36.18  17.06J 

36.10J17.22J 

36.0317.38 

40 

41  37.'l6 

17.33  37.08  17.49 

37.01 

17.65 

36.93  17.81 

41 

42J38.06 

17.75  37.99  17.92 

37.91 

18.08 

37.83  18.25 

42 

43  38.97 

18.17  38.8918.34 

38.81 

18.51! 

38.73  18.681  43 

44|39.88 

18.60  39.8018.77 

39.71 

18.94: 

39.63  19.12 

44 

45140.78  19.02  40.70  19.20  40.62  19.37 
46  41.  69119.44  41.60  19.62  41.52  19.801 

40.53  19.55 
41.43  19.98 

45 
46 

47>42.60  J9.86  42.5120.05 

42.42l20.23 

42.3320.42   47 

48 
49 

43.50 
44.41 

20.29  43.41  20.48 
20.71  144.32  20.90 

43.32 
44.23 

20.66 
21.10' 

43.2320.85 
44.1321.29 

48 
49 

50 

45.32 

21.13J45.2221.33 

45.13 

21.53 

45.0321.72 

50 

1  
Lat.  Dep. 

Dep.| 

Q 

Dep. 

Lat.! 

Dep. 

Lat. 

Lat. 

s 

65  Deg.  '64jDeg. 

64^  Deg. 

64iDeg. 

TRAVERSE  TABLE.                   89 

q 

25  Deg. 

25]  Deg. 

25£l 

)eg. 

25  1  Deg. 

*""l 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.JDep. 

Lat. 

Dep. 

'I 

51 

46.22 

21.55 

46.13 

21.7o'!46.03l2l.96 

45.94 

22.16 

51 

52 

47.13 

21.98 

47.03 

22.  18!  46.93  22.39 

46.84 

22.59 

52] 

53 

48.03 

22.40 

147.94 

22.61 

i47.84!22.82 

47.74 

23.03 

53] 

54 

48.94 

22.82 

48.84  23.03 

'48.7423.25 

48.64 

23.46 

54] 

55 

49.85 

23.24 

49.74  23.46 

49.6423.68 

49.54 

23.89 

5i 

56 

50.75 

23.67 

50.65 

23.89  i50.54  24.111 

50.44 

24.33 

57 

51.66 

24.09 

51.55 

24.31 

:51.45  24.54  51.34 

24.76 

57| 

58 

52.57 

24.51  52.46 

24.74 

52.35  24.97  52.24 

25.20  581 

59  53.47 

24.93 

53.36 

25.17 

53.2525.40 

53.1425.631  59| 

60  54.38 

25.36 

54.27 

25.59  J54.  16  25.83, 

54.0426.07 

.3 

615128 

25.78 

55.17 

26.02 

55.06  26.26!  54.94 

26.50 

61 

6256.1926.20 

56.08 

26.45 

55.8826.69  55.8426.94 

62 

6357.1026.62 
64  58.00l27.05 
65-58.9127.47 
66  59.82  27.89 

56.98 
57.89 
58.79 
59.69 

26.87 
27.30 
27.73 
28.15 

56.8627.12 
57.77  27.65 
58.6727.98 
59.57  28.41 

56.74l27.37 
57.64  27.80 

58.5528.24 
59.4528.67 

6^ 
64 
65] 
66] 

67  60.72 

28.32 

160.60 

28.58 

60.47  28.84 

60.35129.  11 

67 

6861.6328.74 

61.50 

29.01 

61.38  29.27 

61.25129.54 

68 

69162.54I29.16 

62.41 

29.43 

62.2829.71  |62.15!29.98 

69 

70  63.44 

29.68 

163.31 

29.86 

63.18 

30.1463.0530.41    70j 

71  64.35 

30.01 

64.22J30.29 

64.08 

30.67 

63.9530.85    71] 

72  65.25i30.43 

65.  12|30.71 

64.99 

31.00  I64.85l31.28j  72j 

7366.1630.85 

66.0331.14 

65.89 

31.43  65.75i31.71    7$ 

7467.07I31.27 

66.9331.57 

66.79 

31.86  66.65J32.15 

74' 

75 

67.97,31.  7C 

67.83J31.99 

67.69 

32.29  67.55  32.58 

7S 

76 

68.88)32.12 

68.74:32.42 

68.60 

32.72  ;68.45!33.02 

76J 

77 

69.7932.54 

69.64132.85 

69.50J33.15  69.3533.45 

77| 

78 

70.69  32.96 

70.5533.27 

70.4033.58  70.2533.89 

78 

79 

71.60 

33.39j  :71.45  33.  70 

71.30 

34.01  71.16 

34.32 

79 

80 

72.50 

33.81  72.36 

34.13 

72.21 

34.44  72.06 

34.76 

1 

81 

73.41 

34.23 

73.26 

34.55 

73.11 

34.87  72.96 

35.19 

81 

82  74.32 

34.65 

74.17 

34.98 

74.01 

35.30  73.86 

35.62 

82 

83^75.2235.08 

75.07 

35.41 

1  74.91 

35.73  74.7636.06 

83 

84!  76.  13  35.50 

;75.97  35.83 

75.82 

36.16  !75.66  36.49 

84! 

85|  77.04:35.  92  |76.8s!3d.29 
86  77.94  36.35  77.78i36.68 

;  76.7z 
77.62 

36.59  76.3636.93    85 
37.02  77.4637.36    86 

87  78.85i36.77 

78.6937.11 

'78.52l37.45  78.36  37.80!  87j 

8879.7b37.19 

!79.69!37.54 

79.4337.88  79.2638.23 

88 

89 
90 

80.66:37.61  80.50 
81.57  38.04  81.40 

37.96  80.3338.32  80.1638.67   89' 
38.39  81.23;38.75  81.0639.10   90 

91  '82.47  38.46 

82.31 

38.82 

82.1439.18  81.9639.53   91 

92:83.3838.88 

83.21  39.24 

83.0439.61  82.8639.97   92 

9384.29:39.30 

84.1139.67 

83.9440.04  83.7640.40   93 

9485.1939.73 

85.0240.10 

84.8440.47  84.6740.84   94 

9586.1040.15 

85.92140.52 

85.7540.90,85.5741.27 

95] 

96  87.01  40.57 
97  87.91|40.99 

86.83,40.95 
87.7341.38 

86.  65  41.  33  '86.47  41.  71 
87.55  41.  76  i87.37  42.14 

97: 

98  88.82 

41.42 

88.6441.80  88.45 

42.  19  '88.27  42.58 

98 

9989.72 

41.84 

89.5442.23 

89.3642.62 

89.1743.01 

99 

100 

90.63 

42.26  90.45i42.66 

90.2643.05 

90.07  43.44 

100 

tS 

Dep. 

Lat. 

||  j|  !  
Dep.l  Lat.||Dep.  Lat. 

Dep. 

Lat. 

5 

65  Deg. 

643Deg. 

!64> 

Deg. 

64  {  Deg. 

Q| 

TRAVERSE  TABLE. 


O  26  Deg. 

26jDeg. 

26iDeg.  26|Deg.  <-, 

!*  Lat.  Dep. 

Lat.  'Dep. 

Lat. 

Dep.    Lat.  1 

en 
Dep.  r* 

1    0.90  0.44 

0.90!  0.44 

0.89 

0.45    0.89 

0.45     1 

•ft  1.80  0.88 

1.79  0.88 

1.79 

0891    1.79 

0.90     2 

S!  2.70   1.32 

2.69   1.33 

2.68 

I.34J   2.68 

1.35     3 

4i  3.60   1.75 

3.59   1.77 

3.58 

1.78    3.57 

1.80     4 

5  4.49  2.19 

4.48  2.21 

4.47   2.23    4.46   2.25     5 

6   5.39   2.63 

5.38   2.65 

5.37 

2.68    5.36 

2.70;    6 

7   6.29   3.07 

6.28  3.10 

6.26 

3.12J    6.25 

3.15;     7 

8   7.19  3.51 

7.17   3.54 

7.16 

3.571    7.14 

3.60!    8 

9   8.09  3.95 

8.07   3.98 

8.05 

4.021    8.04 

4.05^    9 

10   8.99   4.38!    8.97   4.42 

8.95 

4.46    8.93 

4.50   10 

11   9.89   4.82 

9.87   4.87 

9.84 

4.91    9.82 

Til  n 

1210.79   5.26 

10.76   5.31 

10.74 

5.35  10.72 

5.40   12 

1311.68   5.70 
1412.58   6.14 

11.66   5.7511.63 
12.56   6.19i  12.53 

6.80  11.61 
6.25  12.50 

5.85    13 
6.30    14 

1513.48!  6.58 

13.45    6.63  13.42 

6.69  13.39 

6.75    15 

1614.88!  7.01 

14.35   7.08 

14.32 

7.14  14.29 

7.20    16 

1715.28!  7.45 

15.25   7.-52 

15.21 

7.59  15.18 

7.65    1" 

1816.18!  7.89 

16.14   7.96116.11 

8.03  16.07 

8.10   18 

1917.08'  8.33 

17.04   8.40 

17.00 

8.48  16.97 

8.55    19 

20  17.98;  8.77 

17.94   8.85 

17.90 

8.92  17.86 

9.00  20 

2118.87   9.21 

18.83   9.29 

18.79 

9.37  18.75 

~<K45   21 

2219.77   9.64 

19.73   9.73 

19.69 

9.82  19.65 

9.90   22 

23  20.67  10.08 

20.6310.17 

.20.58 

0.26  20.54 

10.35   23 

2421.5710.52 

21.5210.61 

21.48 

0.71  21.43 

10.80   24 

25  22.47  10.96 

22.4211.06122.37 

11.15  22.32 

11.25   25 

2623.3711.40 

23.32  11.50  23.2" 

11.60  23.22 

11.70   26 

2724.2711.84 

24.2211.94:24.16 

12.05  24.11 

12.15   27 

2825.1712.27 

25.11  12.38  '25.06 

12.49!  25.00 

12.60   28 

2926.0612.71 

26.01  12.  8  * 

25.95 

12.94i  25.90 

13.05   29 

3026.9613.15 

26.91  13.27 

26.85 

13.39  26.79 

13.50  30 

31  27.86  13.59 

27.8013.71 

27.74 

13.83  27.68 

13.95   31 

32  28.76  14.03  28.70  14.15  i28.64 

14.28  28.58 

14.40   32 

3329.66  14.47  29.60  14.60!  29.53 

14.72  29.4 

14.85   33 

3430.56  14.90  '30.49  15.041  30.4 

15.17  30.36 

15.30  34 

35  31.46  15.34  31.39  15.48!  31.3 

15.62  31.2 

15.75   35 

36  32.36  15.78  ;32.29i  15.92;  32.2 

16.06  32.1 

16.20   36 

37|33.26  16.22  !33.1816.36i  33.1 

16.51  33.04 

16.65   37 

38J34.1516.6Q  34.08  16.81  34.0 

16.96  33.9 

17.10   38 

3935.05  17.10  34.98;  17.25  34.9 

17.40  34.8 

17.55   39 

40|35.95;i7.53  135.87  17.69 

35.8 

17.85  35.7 

18.00:  40 

41J36.85  17.97  !36.77  18.13 

36.6 

18.29  36.6 

18.45   41 

4237.75  18.41  37.67  18.58  37.5 

18.74  37.5 

18.90:  42 

43  38.65  18.85  38.57  19.02;  38.4 

19.19  38.4 

19.35  43 

4439.55  19.29  39.46  19.46J  39.3 

19.63  39.2 

19.80!  44 

45  40.45  19.73  40.3649.90  40.2 

20.08  40.1 

20.25!  45 

4641.3420.17  41.2620.35  41.1 

20.53  41.0 

20.70*  46 

4742.2420.60  42.1520.79  42.0 

20.97  41.9 

21.151  47 

48  43.14  21.04  43.05  21.23,  42.9 

21.42  42.8 

21.601  48 

4944.04,21.48  43.9521.67  43.8 

21.86  43.7 

22.05   49 

50  44.94i21.92  ,44.84  22.11  44.7 

22.31  44.6 

22.50   60 

^5  Dep.!  Lat 

.Dep.  Lat 

.|Dep 

Lat.  Dep 

Lat.l^ 

:  co 

S   64  Deg 

.  63f  Deg 

;63iDeg.  63lD€g,P* 

TRAVERSE  TABLE. 


91 


o 

26  Deg. 

26iDeg. 

26i  Deg. 

26}Deg. 

g 

r 

Lat.  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.|Dep. 

r 

51 

45.8422.36 

45.74 

22.56 

45.64 

22.76 

45.5422.95 

51 

52 

46.7422.80 

46.64 

23.00 

46.54 

23.20  46.43  23.41 

52 

53 

47.64  23.23 

47.53 

23.44 

47.43 

23.65ii47.33 

23.86 

53 

54 

48.5323.67 

48.43 

23.88 

48.33 

24.09 

48.22i24.31 

54 

55 

49.4324.11 

49.33 

24.33 

49.22 

24.64 

49.ir24.76 

55 

56 

50.33  24.55 

50.22 

24.77 

50.12 

24.99 

50.01  '25.21 

56 

57 

51.23  24.99 

51.12 

25.21 

51.01 

25.43 

50.9025.66 

57 

58 

52.1326.43 

52.02 

25.65 

51.91 

25.88 

51.79;26.11 

58 

59 

53.03  25.86 

52.92 

26.09 

52.80 

26.33 

52.6926.56 

59 

60 

53.9326.30 

53.81 

26.54 

53.70 

26.77 

53.58;27.01 

60 

61 

54.8326.74 

54.71 

26.98 

54.59 

27.22 

54.47:27.46 

61 

62 

55.7327.18 

55.61 

27.42 

55.49 

27.66 

55.36 

27.91 

62 

63 

56.6227.62 

56.60 

27.86 

56.38 

28.11 

56.26i28.36 

63 

64 

57.5228.06 

57.40 

28.31 

57.28 

28.56 

57.15 

28.81 

64 

65 

58.4228.49 

58.30 

28.75 

58.17 

29.00 

58.04:29.26 

65 

66 

59.32  28.93 

59.19 

29.19 

59.07 

29.45 

58.9429.71 

66 

67 

60.22  29.37 

60.09|29.63 

59.96 

29.90 

59.83!30.16 

67 

68 

61.1229.81 

60.9930.08 

60.86 

30.34 

60.72J30.61 

68 

69 

62.0230.25 

61.8830.52 

61.75 

30.79 

61.62131.06 

69 

70 

62.9230.69 

62.  78130.96 

62.65 

31.23 

62.51J31.51 

70 

i 





71 

63.8131.12 

63.08 

31.40 

63.54 

31.68 

63.4031.96 

71 

72 

64.7131.56 

64.57 

31.84 

64.44 

32.13 

64.29132.41 

72 

73 

65.61  132.  00 

65.47 

32.29 

65.33 

32.57 

65.1932.86 

73 

74 

66.51:32.44 

66.37 

32.73 

66.23 

33.02 

66.0833.31 

74 

75 

67.41:32.88 

67.27 

33.17 

67.12 

33.46 

66.9733.76 

75 

76 

68.3l!33.32 

68.16 

33.61 

68.01 

33.91 

67.8734.21 

76 

77 

69.2133.75 

69.06 

34.06 

68.91 

34.36  68.7634.66 

77 

78 

70.1H34.19 

69.96 

34.50 

69.80 

34.80!  69.65135.  11 

78 

79 
80 

71.0034.63 
71.90l35.07 

70.85  34.94 
71.75  36.38 

70.70 
71.59 

35.25  70.5535.56 
35.70  ,71.44  36.01 

79 
80 

81 


72.80l35.51 

72.6535.83 

72.49 

36.14  72.33J36.46 

81 

82 

73.70*35.95 

73.5436.27 

73.38 

36.59,73.2236.91 

82 

83 
84 

74.60  36.38 
75.5036.82 

74.4436.71 
75.34J37.15 

74.26 
75.17 

:37.03h74.1237.36 
37.48ii75.01  37.81 

83 
84 

85 

76.4037.26 

76.23  37.59 

76.07 

37.93;  75.90  38.26 

85 

86 

77.30i37.70 

77.1338.04 

76.96 

,38.37  76.80j38.71 

86 

87 

78.2038.14 

78.03  38.48 

77.86 

38.82  '77.  69 

39.16 

87 

88 

79.09  38.58 

78.9238.92 

78.75 

39.27  78.58'39.61 

88 

89 

79.99  39.01 

79.82139.36 

79.65 

39.71  1|79.48  40.06 

89 

90 

80.89  39.45 

80.72 

39.81 

80.54 

40.16  80.3740.51 

90 

91 

81.7939.89 

81.62 

40.25 

81.44 

40.60J  81.26 

40.96 

91 

92 

82.6940.33 

32.51 

40.69 

82,33 

41.05  82.15 

41.41 

92 

93 

83.5940.77 

83.41 

41.13 

83.23 

41.50  83.0541.86 

93 

94 

84.4941.21 

84.31 

41.58 

84.  li; 

41.94  83.94142.31 

94 

95 

85.39  41.65 

85.20 

42.02 

85.02 

42.39 

84.  83  142.76 

95 

96 

86.28  42.08 

86.10 

42.46 

85.91 

42.83 

85.7343.21 

96 

97 

87.1842.52 

87.00 

42.90 

86.81 

43.28 

86.6243.66 

97 

98 

88.08  42.96 

87.89 

43.34 

87.70 

43.73 

87.5144.11 

98 

99 

88.98  43.40 

88.79 

43.79 

88.60 

44.17 

88.40144.56 

99 

100 

89.8843.84 

89.69 

44.23 

89.49 

44.62 

89.30)45.01 

100 

+J 

CO 

Dep.    Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

DepJ  Lat. 

ts 

a 

64  Deg. 

63|Deg. 

63iDeg. 

63lDeg. 

Q 

TRAVERSE  TABLE. 


d 

27  Deg.  27^Deg. 

27^Deg. 

273  Deg. 

g 

v> 

Lat. 

Dep. 

Lat. 

Dep. 

,Lat. 

Dep. 

Lat.  Dep. 

w* 

rt- 

I 

0.89 

0.45 

0.89 

0.46 

0.89 

0.46 

0.88 

0.47 

1 

2 

1.78 

0.91     1.78 

0.92 

1.77 

0.92 

1.77 

0.93 

2 

3 

2.67 

1.36    2.67 

1.37 

2.66 

1.39 

2.65 

1.40 

3 

4 

3.56 

1.82    3.56 

1.83 

3.55 

1.85 

3.54 

1.86 

4 

5 

4.45 

2.27|;  4.45 

2.29 

4.44 

2.31 

4.42 

2.33 

5 

6 

5.35 

2.72|1  5.33 

2.75 

5.32 

2.77 

5.31 

2.79 

6 

7j 

6.24 

S.18I'  6.22 

3.21 

6.21 

3.23 

6.19 

3.26 

7 

8 

7.13 

3.63     7.11 

3.66 

7JO 

3.69 

7.08 

3.72 

8 

9 

8.02 

4.09  ;  8.00 

4.12 

7.98 

4.16 

7.96 

4.19 

9 

10 

8.91 

4.54;  8.89 

4.58 

;  8.87 

4.62 

8.85 

4.66 

10 

11 

9.80 

4.99 

9.78   5.04 

1  9.76 

5.08 

9.73 

5.12 

11 

12 

10.69 

5.45  10.67   5.49 

10.64 

6.54 

10.62 

5.59    12 

1311.58 

5.90l  11.56   5.95 

11.53 

6.00 

11.50 

6.05!  13 

1412.47 

6.3612.45   6.41 

12.42 

6.46 

12.39; 

6.52   14 

15;  13.37 

6.81  13.34    6.87 

13.31 

6.93 

13.27! 

6.98    15 

16  14.26 

7.261  114.22   7.33 

14.19 

7.39! 

14.16 

7.45    16 

1715.15 

7.72  15.11    7.78 

15.08 

7.85i 

15.04 

7.921  17 

18  16.04 

8.17JJ16.00   8.24 

15.97 

8.31! 

15.93 

8.38    18 

1916.93 

8.63  J16.89   8.70 

16.85 

8.771 

16.81 

8.85!  19 

20,17.82 

9.08J17.78   9.16 

17.74 

9.23 

17.70 

9.31    20 

L~"~      1 

21 

18.71 

9.53 

18.67   9.62 

18.63 

9.70 

18.58 

9.78   21 

22 

19.60 

9.99  19.66  10.  07  1  19.51 

10.16 

19.47  10.24  22 

23;20.49  10.441:20.45  10.53  20.40  10.62; 

20.35'l0.71   23 

2421.38  10.901  21.34  10.99  21.29  11.08 

21.2411.17!  24 

25  22.28  11.35  22.23  11.45  122.18  11.54 

22.1211.64  25 

26  23.17  11.80  23.11  11.90  '23.06  12.01 

23.01 

12.11:  26 

27124.06  12.261  24.00  12.36  23.95  12.47J 

23.8912.57   27 

2824.95 

12.711  24.89  12.821  24.84  12.93 

24.78  13.04   28 

29  25.84  13.17J  25.78  13.28  !!26.72  13.39! 

25.66 

13.50   29 

3026.73  13.62  26.67  13.74;  26.61  13.85 

26.55  13.97J  30 

31  27.62  14.07  27.56  14.19  '27.50  14.31 

27.43 

14.43   31 

32  28.51 

14.53  28.45  14.65  28.38 

14.78  28.32 

14.90   32 

3329.4014.98  29.34  15.  ll'  29.27  15.24  '29,20  15.37   33 

34  30.29  15.44:  30.23  15.57  30.16  Ib.'tQ  J30.09 

15.83   34 

3531.1915.89  31.  12  16.03!  31.05  16.16  30.97 

16.30j  35 

3632.08  16.34'  32.00  16.48  31.93  16.62,  31.86  16.761  36 
37  32.97  16.801  32.89  18.94  32.82  17.08  32.74|17.23:  37 

38'33.86 

17.25  33.78  17.40  33.71 

17.55 

33.63  17.69   38 

3934.75 

17.71  34.6717.86  34.59  18.01  34.51 

18.16   39 

4035.6418.16  35.56:18.31  35.48  18.47  35.40 

18.62  40 

4136.5318.61 
42'37.42  19.07 
43  38.31  :  19.52 
44  39.201  19.98 
45!40.  10120.43 

36.45 
37.34 
38.23 
39.12 
'40.01 

18.77  36.37  18.93 
19.23  137.25  19.39 
19.69  j38.  14  19.86 
20.15  39.0320.32 
20.60!  39.92  20.  78 

36.28  19.09i  41 
37.17  19.56!  42 
38.05  20.02  43 
38.  941  20.  49   44 
39.8220.95   45 

4640.9920.88 

!40.88 

21.06;  40.80l21.24 

40.7121.42   46 

4741.8821.34 

141.7S 

21.52  41.69  21.70 

41.5921.88   47 

4342.77 
4943.66 
5044.5£ 

21.79 

22.25 
22.70 

^.eT 

143.56 
44.4c 

21.98142.5822.16 
22.44  43.46  22.63 
22.89  144.35  23.09 

42.48!22.3t 
43.3622.85 
44.25  23.2i 

>|  48 
>   49 
5   50 

•*J 

Dep. 

Lat. 

Dep 

Lat.  Dep 

Lat. 

Dep. 

Lat 

"8 

63 

Deg. 

62'Deg.|!62iDeg. 

62iDeg 

(2 

TRAVERSE  TABLE. 


93 


•o 

27  Deg. 

27iDeg. 

27iDeg. 

27fDeg. 

e 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

CO 
p*- 

51 

45.44 

23.15 

45.34 

23.35 

45.24 

23.55 

45.13 

23.75 

51 

52 

46.33 

23.61 

48.23S23.81 

46.12 

24.01 

46.02 

24.21 

52 

53 

47.22 

24.06 

47,1224.27 

47.01 

24.47 

46.90 

24.68 

53 

54 

48.11 

24.52 

48.01  124.73 

47.90 

24.93 

47.79125.14 

54 

55 

49.01 

24.97 

48.9025.18 

48.79  25.40 

48.67j25.61 

55 

56 

49.90 

25.42 

49.7825.64 

49.67i25.86 

49.56126.07 

56 

57 

50.79 

25.88 

50.6726.10 

50.56  '26.32 

50.44  26.54 

57 

58 

51.68 

26.33 

51.5626.56 

51.45126.78 

51.33  3^01 

!  58 

59 

52.57 

26.79 

52.45  27.01 

52.3327.24 

52.21  27.47 

59 

60 

53.46 

27.24 

53.34  27.47 

53.2227.70 

53.1027.94   60 

61 

54.35 

27.69 

53.2327.93 

54.1128.17  53.98J28.4oi  61 

62 

55.24 

28.15 

55.1228.39 

54.99l28.63 

54.8728.87   62 

63 

56.13 

28.60 

56.01  28.85 

55.8829.09  55.7529.33   63 

64 

57.02 

29.06 

56.90  29.30 

56.7729.55  56.6429.80   64 

65 

57.92 

29.51 

57.7929.76 

57.66  30.01  '57.52  30.26   65 

66 

58.81 

29.96 

58.68  30.22 

58.5430.48  58.4130.73   66 

67 

59.70 

30.42 

59.5630.68 

59.4330.94  59.2931.20   67 

68 

60.59 

30.87 

60.4531.14 

60.3231.40  60.1831.66   68 

69 

61.48 

31.33 

61.3431.59 

61.2031.86  61.0632.13   69 

70 

62.37 

31.78 

62.2332.05 

62.0932.32  61.95  32.59;  70 

71 

63.26 

32.23 

|  
63-1232.51 

_               '             a_,m_m'  -    J  

62.98  32.  78'  !62.83  33.06    71 

72 

64.15 

32.69 

64.0132.97 

63,8633.25  63.7233.52   72 

73 

65.04 

33.14 

64.9033.42 

64.7533.71  64.6033.99;  73 

74 

65.93 

33.60 

65.79  33.88 

65.6434.17  65.4934.46   74 

75 

66.83 

34.05 

66.68  34.34 

66.5334.63  66.3734.92   75 

76 

67.72 

34.50 

67.57  34.80 

67.4135.09  67.2635.39    76 

77 

68.61 

34.96 

68.4535.26 

68.30  35.55  68.  14  35.85   77 

78 

69.50 

35.41 

69.3435.71 

69.1936.02  69.0336.32:  78 

79 

70.39 

35.87 

70.2336.17 

70.0736.48  69.9136.78   79 

80 

71.28 

36.32 

71.12:36.63 

70.9636.94  70.8037.25   80 

81 

72.17 

36.77 

72.0137.09 

71.8537.40  71.6837.71 

81 

82 

73.06 

37.23 

72.9037.55 

72.7337.86  72.5738.18   82 

83 

73.95 

37.68 

73.7938.00 

73.6238.33  73.4538.65   83 

84 

74.84 

38.14 

74.68'38.46 

74.5138.79  74.3439.11 

84 

85 

75.74 

38.59 

75.57  38.92 

75.4039.25  75.2239.58   85 

86 

76.63 

39.04 

76.46  39.38 

76.2839.71  76.1140.04   86 

87 

77.52 

39.50 

77.3439.83 

77.1740.17  76.9940.51 

87 

88 

78.41 

39.95 

78.23:40.29 

78.0640.63  77.8840.97    88 

89 

79.30 

40.41 

79.1240.75 

78.9441.10  78.7641.44   89 

90 

80.19 

40.86 

80.01 

|41.tl 

79.8341.56  79.6541.91 

90 

91 

81.08 

41.31 

80.9041.67 

80.7242.02  80.5342.37   91 

92 

81.97 

41.77 

81.7942.12 

81.6042.48  81.4242.84   92 

93 

82.86 

42.22 

82.68  42.58 

82.4942.94  82.3043.30   93 

94 

83.75 

42.681  183.57  43.04 

83.3843.40  83.1943.77    94 

95 

84.65 

43.13 

84.46  43.50 

84.27  43.87 

84.0744.23    95 

96 

85.54 

43.58185.3543.96 

85.1544.33 

84.9644.70:  96 

97 

86.43 

44.04ii86.23  44.41 

86.0444.79 

85.84  45.16!  97 

98 

87.32 

44.49  ;87.  12  44.87 

86.93  45.25 

86.7345.63 

98 

99 

88.21 

44.95  88.0145.33 

87.81  45.71 

87.6146.10   99 

100 

89.10 

45.40 

88.9045.79 

88,7046.17 

88.5046.56100 

oj 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

Lat. 

-s 

5 

63  Deg. 

624n<->. 

62  1  Deg. 

62J  Deg. 

£ 

TRAVERSE  TABLE. 


« 

28  Deg. 

28^  Deg. 

28£Deg. 

284'Deg. 

s 

r 

Lat. 

Dep. 

Lat.  Dep. 

Lat.lDep. 

Lat. 

Dep. 

r 

i 

0.88 

0.47 

0.88   0.47 

0.88 

0.48 

0.88 

-0.49 

\ 

2 

1.77 

0.94 

1.76   0.95 

1.76 

0.95 

1.75 

0.96 

2 

3 

2.65 

1.41 

2.64    1.42 

2.64 

1.43 

2.63 

1.44 

3 

4 

3.53 

1.88 

3.52    1.89 

3.52 

1.91 

3.51 

L92 

4 

5 

4.41 

2.35 

4.401  2.37 

4.39 

2.39 

4.38   2.40 

5 

6 

5.30 

2.82 

5.29   2.84 

5.27 

2.861 

5.261  2.89 

6 

7 

6.18 

3.29 

6.1*  3.31 

6.15 

3.34| 

6.14 

3.37 

6 

7J8.S 

3.76 

7.05;  3.79 

7.03 

3.82J 

7.011  3.85 

8 

9 

7.95 

4.23 

7.93   4.26 

7.91 

4.29 

7.89 

4.33 

9 

10 

8.83 

4.69 

8.81    4.73 

8.79 

4.77 

8.77 

4.81 

ie 

11 

9.71 

5.16 

9.69   5.21 

9.67 

5.25 

9.64 

5.29 

11 

12 

10.60 

5.63 

10.57    5.68 

10.55 

5.73 

10.52 

5.77 

12 

13 

11.48 

6.10 

11.45   6.151  11.42 

6.20 

11.40 

6.25 

13 

14 

12.36 

6.57 

12.33    6.63i  12.30 

6.68 

12.27 

6.73 

14 

15 

13.24 

7.04 

13.21    7.10  13.18 

7.16 

13.15 

7.21 

15 

16 

14.13 

7.51 

14.09    7.57 

14.06 

7.63 

14.03 

7.70 

16 

17 

15.01 

7.98 

14.98   8.05  14.94 

8.11 

14.90 

8.18 

17 

18 

15.89 

8.45 

15.86   8.52J  15.82 

8.59 

15.78 

8.66 

18 

19 

16.78 

8.92 

16.74   8.99  16.70 

9.07 

16.66 

9.14    19 

20 

17.66 

9.39 

17,62   9.47 

:  17.58 

9.54 

17.53 

9.62 

20 

21 

18.54 

9.86 

18.50  9.94 

18.46  10,02 

18.41 

HUO!  21 

22 

19.42 

10.33 

19.38  10.41 

19.3310.50 

19.29  10.581  22 

23 

20.31 

10.80 

20.26  10.89 

20.21 

10.97 

20.1611.06   23 

24 

21.19 

11.27 

21.1411.36  21.0911.45 

21.0411.54 

24 

25 

22.07 

11.74 

22,02  11.83  21.97  11.93 

21;92  12.02   25 

26 

22.96 

12.21 

22.9012.31  22.8512.41 

22.7912.51    26 

27 

23.84 

12.68 

2S.78  12.78 

23.7312.88 

23.67 

12.991  27 

28 

24.72 

13.15 

24.66  13.25 

124.61 

13.36 

24.55  13.47 

28 

29 

25.61 

13.61 

25.55  13.73 

25.49  13,84 

25.43  13.95 

29 

30 

26.49 

14.08 

26.43  14.20 

26.36  14.31 

26.30  14.43 

38 

81 

27.37 

14.55 

27.31  14.67 

27.2414.79 

27.18  14.91 

31 

32 

28.25 

15.02 

28.1915.15 

28.1215.27 

28.06  15.39 

32 

33 

29.14 

15.49 

29.07  15.62 

29.00  15.75 

28.93  15.87 

33 

34 

30.02 

15.96 

29.9516.09 

29.88  16.22 

29.81 

16.35 

34 

35 

30.9(1 

16.43 

30.83  16.57 

30.76  16.70 

30.69  16.83 

35 

36 

31.79 

16.90 

31.71  17.04 

31.6417.18 

31.5617.32 

36 

37 

32.67 

17.37 

32.59  17.51  132.52  17.65 

32.44  17.801  37 

38 

33.55 

17.84 

33.47  17.99 

33.3918.13 

33.32  18.28 

38 

39 
40 

34.43 
35.32 

18.31 

18.78 

34.35  1S.46 
35.24  1».93 

34.27  18,61 
B&X5  19.09 

34.19 
35.07 

18.76 
19.24 

39 
40 

41 

36.20 

19.25 

36.1219.41 

36.03  19.56 

35.95  19.72 

41 

42 

37.08 

19.72 

37.0019.88 

36.91  20.04 

36.82  20.20 

42 

43 

37.97 

20.19 

37.8820.35 

137.7920.52 

37.7020.68   43 

44 

38.85 

20.66 

38.7620.83  38.6720.99 

38.5821.16   44 

45 

39.73 

21.13 

39.64  21.30!  139.55  21.  47 

39.4521.64   45 

46 

40.62 

21.60 

40.52  21.77 

40.4321.95 

40.3322.13   46 

47 

41.50 

22.07 

41.4022.25 

J41.30  22.43 

41.21  22.61J  47 

46 

42.38 

22.53 

42.28  22.72 

42.1822.90 

42.0823.09   48 

49 

43.26 

23.00 

43.1623.19 

43.06  23.38 

42.96  23.57 

49 

50 

44.15 

23.47 

44.04  23.67 

43.94  23.86 

43.84  24.05 

50 

-*-* 

Dep. 

Lat. 

DepJ  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

•4-1 

5 

6H 

G 

62  Deg. 

leijDeg. 

GliDeg. 

Deg. 

TRAVERSE  TABLE 


o  28  Deg.  j  28peg.  |28iDeg.|  28f  Deg.j  Q 

«•  Lat. 

Dep.j  Lat.|Dep.  j  Lat. 

Dep.  |  Lat. 

j 

51  45.03,23.94  44.  93:  24.  14^44.  82 
5245.91124.41  45.81  24.61  45.70! 

24.34  44.71 
24.81  45.59 

24.53)  51 
25.01    52 

53  46.80i24,88  46.69:25.09!  46.58|25.29i  46.47 

25.49   53 

54,47.68  25.35  47.57i25.56  47.46i25.771  47.34 

25.97;  54 

5548.56 

25.82  48.45!26.03;  48.3326.24  48.22 

26.45|  55 

56  49.45 

26.29  49.33i26.51  49.21  26.72!  49.10 

26.94   56 

57  50.33f26.76  60.21J26.98  50.09|27.20  49.97 

27.42   57 

58  51.21  J27.23  51.09l27.45  50.97127.68  50.85 

27.90   58 

59  52.09;  27.  70  51.97:27.93  51.8528.15  51.73 

28.38   59 

6052.9828.17  52.85|28.40  52.73 

28.63  52.60 

28.86   60 

61  53.86  28,64  53.73'28.87  53.61 

29.11  53.48 

29.34   61 

6254.7429.11  54.6229.35  54.49 

29.58  54.36 

29.82   62 

63  55.63,29.58  55.50  29.82  55.37 
64156.5130.05  56.3830.29  56.24 

30.06  55.23 
30.54  66.11 

30.30   63 
30.78;  64 

65157.3930.52  57,2630.77  57.12 

31.02  56.99 

31.26   65 

66J58.27  30.99  58.1431.24  58.00 

31.49  57.86 

31,75   66 

67  59.16  31.45  59.02:31.71i  58.88 

31.97  58.74 

32.23   67 

6860.0431.92  59.90  32.19  59.76 

32.45  59.62 

32.71    68 

6960.9232.39  60.  78!32.66  60.64 

32.92  60.49 

33.191  69 

7061.81 

32.86  61.66 

33.13  61.52 

33.40  61.37 

33.67    70 

71  62.69 

33.33  62.54  33.61!  62.40 

33.88  62.25 

34.15   71 

7263.5733.80  63.4234.08  63.27 

34.36  63.12 

34.63   72 

73  64.46!34.27  64.30i34.55  64.15 

34,83  64.00 

35.11    73 

7465.3434.74  65.1935.03  65.03 

35.31  64.88 

35.59   74 

75166.22:35.21  66.07  35.50  65.91 

35.79  65.75 

36.07   75 

7667.1035.68  66.95'35.97  66.79 

36.26  66.63 

36.56    76 

77^7.99  36.  15  67.83136.45  67.67 

36.74  67.51 

37.04   77 

7868.8736.62  68.7136.92  68.55 

37.22  68.38 

37.52    78 

7969.7537.09  69.5937.39  69.43 

37.70,  69.26 

38.00   79 

8070.6437.56  70.47 

37.87  70.31 

38.17  70.14 

38.48   80 

—  :  

81  71.5238.03  71.35 

38.34  71.18 

38.65  71.01 

38,96   81 

8272.4038.50  72.2338.81  72.06 

39.13  7L89 

39.441  82 

8373.2838.97  73.11  39.29  72.94 

39.60  72.77 

39.92   83 

8474.1739.44  73.9939.76  73.82 

40.08  73.64 

40.40   84 

8575.0539.91  74.8840.23  74.70 

40,56  74.5240.88   85 

86  7&.93  40.37  75.7640.71  75.58 

41.04  75.40 

41.36   86 

87  76.8240.84  76.6441.18  76.46 

41.51  76,28 

41.85   87 

8877.7041.31  77.5241.65  77.34 

41.99  77.15 

42.33   88 

89  78.58  41.78  78.40  42.13  78.21 

42.47  78.03 

42.81    89 

90  79.47  42.25  79.28;42.60  79.09 

42.94  78.91 

43.29   90 

91  80.3542.72  80.1643.07  79.97 

43.42  79.78 

43.77   91 

9281.23143.19  81.0443.55  80.85 

43.90  80.66144.25   92 

9382.lll43.66  81.9244.02  81.  73)44.38  81.54 

44.73   93 

9483.0044.13  82.8044.49  82.61 

44.85  82.41 

45.21    94 

9583.8844.60  83.6844.97  83.4945.33  83.2945.69    96 

95  84.  7«!45.07  84.57  45.44  84.3745.81  84.1746.17   96 

97  85.65  45.54  85.45  45.91  85.25 

46.28  85.0446.66   97 

9886.5346.01  86.3346.39  86.12!46.  76  85.92i47.14   98 

99  87.41 

46.48  87.21 

46.86  87.0047.24  86.80:47.62   99 

100  88.2J 

1146.95  88.09  47.33  87.88J47.72  87.67j48.10  WO 

^J  Dep 

QD 

Lat.  Dep.   Lat.  lDep.|  Lat.  Dep. 

Lat.^ 

96 


TRAVERSE  TABLE. 


^29  Deg. 

29iDeg. 

29£L)eg. 

29£Deg. 

q 

•*  Lat.  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.   r" 

1    0.87  0.48 

0.87 

0.49 

0.87 

0.49 

0.87 

0.501     1 

2    1.75   0.97 

1.74 

0.98 

1.74 

0.98 

1.74 

0.99     2 

3   2.62    1.45 

2.62 

1.47 

2.61 

1.48 

2.60 

1.49 

« 

4   3.50!  1.94 

3.49 

1.95 

3.48 

1.97 

3.47 

1.98i     4 

5   4.37J  2.42 

4.36 

2.44 

4.35 

2.46 

i  4.34 

2.48 

6   5.251  2.91 

5.23 

2.93 

5,22 

2.95 

5.21 

2.98 

i 

7    6.12   3.39 

6.11 

3.42 

6.09 

3.45 

6.08 

3.47 

8    7.00 

3.88 

6.98 

3.91 

6.96 

3.94 

6.95 

3.97 

1 

9    7.87 

4.36 

7.85 

4.40 

7.83 

4.43 

7.81 

4.47J     9 

10   8.75 

4.85 

8.72 

4.89 

8.70 

4.92 

8.68 

4.96 

10 

11~9JB2 

5.33 

9.60 

5.37 

9.57 

5.42 

9.55 

5.46 

1210.50 

5.82 

10.47 

5.86 

10.44 

5.91 

10.42 

5.95 

c 

13i  11.37 

6.30 

11.34 

6.35 

11.31 

6.40 

11.29 

6.45,     3 

14|  12.24 

6.79 

12.21 

6.84 

12.18 

6.89 

12.15 

6.95!     4 

1513.12 

7.27 

13.09 

7.33 

13.06 

7.39 

13.02 

7.44     5 

1613.99 

7.76 

13.96 

7.82 

13.93 

7.88 

13.89 

7.94     6 

17j  14.  87 

8.24 

14.83 

8.31 

14.80 

8.S7 

14.76 

8.44 

7 

1815.74 

8.73 

15.70 

8.80 

15.67 

8.86 

15.63 

-8.93 

g 

1916.62 

9.21 

16.58 

9.28 

16.54 

9.36 

16.50 

9.43 

i 

2017.49    9.70| 

17.45 

9.77 

17.41 

9.85 

17.36 

9.92 

20 

2118.3710.18 

18.32 

10.26 

18.28 

10.34 

18.23 

10.42 

21 

22j  19.24  10.  67 

19.19 

10.75 

19.15 

10.83 

19.10 

10.92 

22 

2320.12jll.15 

20.07  11.24 

20.02 

11.33 

19.97 

11.41 

23 

24  20.99  11.64 

20.9411.73 

20.89 

11.82 

20.84 

11.91 

24 

25:21.8712.12 

21.81112.22 

21.76 

12.31 

21.70 

12.41 

25 

2622.7412.60 

22.68  12.70 

22.63 

12.80 

22.57 

12.90 

26 

2723.6M3.69l 

23.5613.19 

23.50 

13.30 

23.44 

13.40 

27 

28I24.49  13.571 

24.43jl3.68 

24.37 

13.79 

24.31 

13.89 

28 

29|25.36  14.06 

25.3014.17 

25.24 

14.28 

25.18 

14.39 

29 

39126.24  14.54 

26.1714.66 

26.11 

14.77 

26.05 

14.89 

30 

_  
31J27.11 

15.03 

27.05  15.15 

26.98 

15.27 

26.91 

15.38 

31 

3227.99 
3328.86 

15.51!  27.92 
16.00  28.79 

15.64 
16.12 

27.85 
28.72 

15.76  27.78 
16.25  28.65 

15.88 
16.38 

32 
33 

34  29.74  16.481 
3530.6116.971 

29.66 
30.54 

16.61 
17.10 

29.59 
30.46 

16.74 
17.23 

29.52 
30.39 

16.87 
17.37 

34 
35 

36  31.49  17.45 

31.41 

17.59 

31.33 

17.73 

31.26 

17.86 

36 

37  32.36i  17.94 

32.28ll8.08 

32.20 

18.22 

32.12 

18.36 

37 

38,33.24118.421 

33.1518.57 

33.07 

18.71 

32.99 

18.86 

38 

3934.11J18.91 

34.0319.66 

33.94 

19.20 

33.86 

19.35 

39 

4034.98.  19.39 

34.9019.54 

34.81 

19.70 

34.73 

19.85 

40 

4135.86 

19.88 

35.7720.03 

35.68 

20.19 

35.60 

29.34 

41 

42  36.73  20.36 

36.64'20.52 

36.55 

20.68 

05.46 

20.84 

42 

4337.6120.85  37.52i21.01 

37.43  21.171 

37.3.'i 

21.34 

43 

4438.48:21.33, 

38.39j21.50 

3S.30  21.67!  38.20 

21.83 

44 

4539.3621,82 

39.26  21.99 

39.17 

22.16139.07 

22.33, 

45 

4640.23 

22.30  40.13122.48 

40.04 

22,65 

39.94 

22.83J 

46 

4741.11 

22.79 

41.01  22.97 

40.91 

23.14 

40.81 

:3.32J 

47 

4841.98 

23.27 

41.88  23.45 

41.78 

23.63 

41.67 

23.82J 

48 

49  42.86 

23.76!  ,42.  75,23.94 

42.65 

24.13i 

42.54 

24.31! 

49 

5043.73 

24.241 

43.6224.43 

43.52 

24.62 

43.41 

24.81J 

60 

+1  Dep. 

1 
Lat.  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.!^ 

5  i  61  Deg. 

60fDeg. 

60jDeg. 

60  'Deg  Q 

TRAVERSE  TABLE* 


Vj29  Deg.  29£Deg. 

29^-Deg. 

29£  Deg. 

g 

r 

Lat.  Dep.    Lat.;Dep. 

Lat.|Dep. 

Lat.  Dep. 

09 
t-t- 

5l'44.61  24.73  44.5024.92 
52  45.48  25.211  45.37  25.41 

44.3925.11 
45.2625.61 

44.2825.31 
45.  15  125.80 

51 

52 

53  46.35  25.69!  46.24  25.90 

46.1326.10 

46.0126.30 

53 

5447.2326.18  47.1126.39 

47.0026.59 

46.8826.80 

54 

5548.1026.66  47.9926.87 

47.87!27.08 

47,7527.29 

55 

5648.9827.15:48.8627,36 

48.7427.58 

48.62|27.79 

56 

5749.8527.63  49.7327.85 

49.61  28.07 

49.4928.28 

57 

5350.7328.12  50.6028.34 

50.48  28.56 

50.3628.78 

58" 

5951.6028.60  51.4828.83 

51.3529.05 

51.2229.28   59 

60  52.48  29.09,  52.35  29.32 

52.2229.55 

52.0929.77 

60 

6ll53.35  29.57  53.2229.81 

53.0930.04 

52.96'30.27 

61 

62i54.23  30.06  54.09  30.29 

53.96  30.53 

53.8330.77 

62 

63'55.  10  30.54  54.9730.78 

54.8331.02 

54.7031.26 

63. 

64  55.98  31.03  55.84  31.27 

55,7031.52 

55.56  31.76 

64 

65  56.85  31.51  56.71  31.76 

56.5732.01 

56.43  32.25 

65 

6657.7232.00  57.5832.25 

57.4432.50 

57.3032.75 

66 

67|58.60  32.48  58.4632.74 
68  59.47  32.97  59.3333.23 

58.31  32.99 
59.1833.48 

58.1733.25 
69.0433.74 

67 

68 

69  60.35  33.45'  60.20  33.71 

60.05  33.98 

59.91  34.24 

69 

70  61.22  33.94!  61.07  34.20 

60.9234.47 

60.77j34.74 

70 

Jj  '  : 
71|62.10  34.421  61.95  34.69 

61.8034.96 

1  
61.6435.23 

71 

72 
73 

62.9734.91  62.8235.18 
63.8535.39  63.6935.67 

62.67  35.45 
63.5435.95 

62.51!35.73 
63.38  36.22 

72 
73 

74 

64.7235.88  64.5636.16 

64.41  36.44 

64.2536.72 

74 

75 

65.6036.36  65.4436.65 

65.28  36.93 

65.1137.22 

75 

76 

66.4736.85:66.3137.14 

66.1537.42 

65.98  37.71 

76 

77 

67.3537.33  67.1837.62 

67.02  37.92 

66.85  38.21 

77 

78 

68.2237.82  68.0538.11 

67.89  38.41 

67.7238.70 

73 

79 

69.09  38.30:  68.93  38.60 

68.7638.90 

68.5939.20 

79 

60 

69.97j38.  78:  69.80  39.09 

69.63  39.39 

69,4639.70 

80 

81 

70.8439.27  70.6739.58 

70.5039.89 

70.3240.19 

81 

82 

71.72:39.  75!  71.54  40.07 

71.37  40.38 

71.1940.69 

82 

83 

72.5940.24  72.4240.56 

72.2440.87 

72.0641.19 

85 

84 

73.47  40.72!  73.29  41.04 

73.1141.36 

72.93  41.68 

84 

85 

74.3441.21  741641.53 

73.9841.86 

73.8042.18 

85 

86 

75.2241.69  75.0342.02 

74.8542,35 

74.67  42.67 

86 

87 

76.09|42.18  75.9ll42.51 

75.7242.84 

75.5343.17 

87 

88 

76.97;42.66  76.78!43.00 

76.59  43.33 

76.4043.67 

86' 

89 

77.84!43.15j  77.6543.49! 

77.4643.83 

77.27  44.16 

89 

90 

78.72j43.63  78.52:43.98( 

78.3344.32 

78.1444.66 

90 

91 

79.59J44.12  79.4044.461 

79.20!44.81 

79.0145.16 

91 

92 

80.46J44.60;  80.27  44.95 

80.07i45.30 

79.8745.65 

92 

93 

81.3445.09  81.1445.44 

80.94'45.80 

80.7446.15 

93 

94 

82.21  45.57,  82.01  45.93 

81.8146.29 

81.6146.64 

94 

95 

83.09  46.06  82.89  46.42 

82.68:46.78 

82.4847.14 

95 

96 

83.96j46.54!  83.7646.91  83.5547.27 

83.35  47.64 

9ti 

97 

84.8447.03'  84.63:47.40  84.42  47.77 

84.2248.13 

97 

98 

85.71  47.51  85.5047.88  !85.2948.26 

85.08  48.63 

98 

99 

86.5948.00  86.38J48.37  86.17:48.75 

85.9549.13 

9$ 

100 

87.4648.48  87.2548.86, 

1 

87.0449.24 

86.8249.62 

loo- 

-*J 
QQ 

Dep.  Lat.  Dep.l  Lat. 

DepJ  Lat. 

Dep.  Lat. 

's 

a 

61   Deg.  60£  Deg. 

60£Deg. 

60iDeg. 

s 

98 


TRAVERSE  TABLE. 


t-j'30  Deg. 

5.  .  — 

30£  Deg.  j  30£  Deg. 

30£Deg. 

O 

r 

Lat. 

Dep. 

Lat.iDep. 

Lat. 

Dep. 

Lat. 

Dep. 

5" 

«•*• 

i 

0.87 

0.50 

0.86   0.50 

0.86 

0.51 

0.86 

0.51 

1 

2 

1.73 

1.00 

1.73 

1.01 

1.72 

1.02 

1.72 

1.02 

2" 

3 

2.60 

1.50 

2.59|  1.51 

2.58 

1.52 

2.58 

1.53 

t 

4 

3.46 

2.00 

3.46 

2.02 

3.45 

2.03 

3.44 

2.05 

4 

5 

4.33 

2.50 

4.32 

2.52    4.31 

2.54 

4.30 

2.56 

t 

6 

5.20  3.00 

5.18 

3.02    5.17 

3.05 

5.16 

3.07 

e 

7 

6.06 

3.50 

6.05 

3.53    6.03 

3.55 

6.02 

3.58 

7 

8 

6.93 

4.00 

6.91 

4.03  !  6.89 

4.06 

6.88 

4.09 

8 

9 

7.79 

4.50 

7.77 

4.53 

7.75 

4.57 

7.73 

4.60 

9 

10 

8.66 

5.00 

8.64 

5.04 

8.62 

5.08 

8.59 

6.11 

10 

11 

9.53 

5.50 

9.50 

5.54 

9.48 

5.58 

9.45 

5.62 

11 

12  10.39 

6.00 

10.37J  6.05 

10.34 

6.09  10.31 

6.14 

12 

13  11.26 

6.50 

11.23 

6.55 

11.20 

6.60 

11.17 

6.65 

13 

14  12.12 

7.00 

12.09 

7.05 

12.06 

7.11  12.03 

7.16 

14 

1512.99 

7.50 

12.96 

7.66 

12.92 

7.61  112.89 

7.67 

15 

1613.86 

8.00 

13.82 

8.06 

13.79 

8.12  13.75 

8.18 

16 

17 

1472 

8.50 

14.69 

8.56  14.65 

8.63  14.61 

8.69 

17 

18'  15.59 

9.00 

15.55 

9.07  15.51 

9.1415.47   9.20 

18 

1916.45 

9.50 

16.41 

9.57  16.37 

9.64  16.331  9.71 

19 

2017.3210.00 

17.28.10.08  17.23 

10.15  17.19J10.23 

20 

21 

18.19  10.50 

18.  14;  10.58  18.09 

10.66 

18.05'  10.74   21 

22;  19.05 

11.00 

19.0011.08  18.96 

11.17  18.9l!ll.25   22 

23 

19.92  11.50 

19.87 

11.59  19.8211.67  19.7711.76   23 

2420.7812.00 

20.  73112.09  20.68ll2.18  20.6312.2?:  24 

2521.6512.50 

21.6012.59  '21.  54'|  12.69  21.49 

12.78   25 

26 

22.52  13.00 

22.4613.10  22.40  13.20  !22.34  13.29   26 

2723.3813.50 

23.32  13.60  :23.26;13.70  23.20!l3.80   27 

28-24.25 

14.00 

24.  19 

14.11  24.  13!  14.21  24.06  14.32   28 

2925.11 

14.50 

25.0514.61  24.99  14.72  24.921  14.83   29 

30  25.98 

15.00 

25.9215.11 

25.85 

15.23  25.78  15.34;  30 

3126.8515.50 

26.7815.62 

26.71 

15.73'  26.64  15.85   SI 

32127.71 

16.00 

27.6416.12 

27.57116.24,27.50  16.36;  32 

33  28.58  16.50 

28.51 

16.62 

28.43  16.75  28.36  16.87:  33 

34129.44  17.00 

29.37 

17.13 

29.3017.26  29.22  17.38J  34 

35|30.31  17.50 

30.23 

17.63 

30.16ll7.76  30.08  17.901  35 

36131.18.18.00 

31.10 

18.14  31.02!18.27  30.94  18.411  36 

37  32.04!  18.50 
3832.9119.00 

31.96 

32.83 

18.64  31.88 
19.14  ,32.74 

18.78  31.80  18.92   37 
19.29  32.66  19.43    38 

3933.7719.50 

33.69 

19.65  33.60 

19.79  33,52  19.941  39 

40 

34.6420.00 

34.55 

20.151  34.47 

20.30' 

: 

34.3820.45  40 

41 

35.51  20.50 

35.42  20.  651  35.33 

20.81 

35.24  20.96I~41 

42 

36.37l21.00 

36.28J21.16;  ,36.  19 

21.32  |36.  10  21.47   42 

43 

37.2421.50 

37.1421.66  37.05 

21.82:36.9521.99    43 

$ 

38.1122.00 
38.97  22.50 

38.0122.17  37.91 

38.8722.67  38.77 

22.33J  37.81  22.50   44 
22.8438.6723.01    45 

46  39.  84123.00 

39.74 

23.17|39,63 

23.35  39.53!23.52i  46 

4740.7023.60 

40.60 

23.68  J40.50 

23.85  40.39!24.03   47 

48  41.57  24.00 

41.46 

24.18  41.36 

24.36  41.2524.54   48 

4942.4424.50 

42.3324.68  42.22 

24.87: 

42.1125.05  49 

50 

43.30 

25.00 

43.19 

26.19 

43.08 

25.38 

42.9725.56  50 

3 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

H!~ 

De~p7 

Lat^ 

5 

60  Deg. 

59fDeg. 

59iDeg. 

59iDeg.2 

TRAVERSE  TABLE. 


99 


030  Deg.  |30£Deg. 

301  Deg. 

SO^  Deg. 

e 

r 

Lat. 

Dcp.    Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

&' 

5l'44.17 

25.50  44.06 

25.69 

43.94  25.88 

43.83 

26.08 

51 

52,45.03 

26.00  44.92 

26.20 

44.8026.39 

44.69 

26.59 

52 

5345.90 

26.50  45.78 

26.70 

45.6726.90 

45.55 

27.10 

53 

54:46.77 

27.00  46.65 

27.20 

46.5327.41 

46.41 

27.61 

54 

5547.63 

27.50  47.51 

27.71 

47.39 

27.91 

47.27 

28.12 

55 

56148.50 

28.00!  48.37 

28.21 

48.25 

28.42 

48.13 

28.63 

56 

5749.36 

28.50  49.24 

28.72 

49.11 

28.93 

48.99 

29.14 

57 

5850.23 

29.00!  50.  10 

29.22 

49.97  29.44 

49.85 

29.65 

58 

5951.10 

29.50!50.97 

29.72 

50.8429.94 

50.70 

30.17 

59 

60,51.96 

30.00:  51.83 

30.23 

51.7030.45 

51.56 

30.68 

60 

6V52.83 

30.50i  152.69 

30.73 

52.56  30.96 

52.42 

31.19 

61 

62  53.69 

31.00  53.56 

31.23 

53.42  31.47 

53.28 

31.70 

62 

63  54.56 

31.50:54.42 

31.74 

54.2831.97 

54.14 

32.21 

63 

64  55.43 

32.00  55.29 

32.24 

55.1432.48 

55.00 

32.72 

64 

65  56.29 

32.50  56.15 

32.75 

56.01  32.99 

55.86 

33.23 

65 

6657.16 

33.00  57.01 

33.25 

56.87  33.50 

56.72 

33.75 

66 

6758.02 

33.50  57.88 

33.75 

57.7334.01 

57.58 

34.26 

67 

68,58.89 

34.00  58.74 

34.26 

58.5934.51 

58.44 

34.77 

68 

6959.76 

34.50  59.60 

34.76 

59.4535.02 

59.30 

35.28 

69 

70J60.62 

35.00  60.47 

35.26 

60.3135.53 

60.16 

35.79 

70 

71  61.49 

35.50  61.33 

35.77 

61.1836.04 

61.02 

36.30 

71 

7262.35 

36.00  62.20 

36.27 

62.0436.54 

61.88 

36.81 

72 

73163.22 

36.50  63.06 

36.78 

62.9037.05 

62.74 

37.32 

73 

7464.09 

37.00  63.92 

37.28 

63.7637.56 

63.60 

37.84 

74 

75  64.95 

37.50  64.79 

37.78 

64.6238.07 

64.46 

38.35 

75 

76  65.82 

38.00  65.65 

38.29 

65.48  38.57 

65.31 

38.86 

76 

77  66.68 

38.50  66.52 

38.79  66.3539.08 

66.17 

39.37 

77 

78  67.55 

39.00  67.38 

39.29  67.2139.59 

67.03 

39.88 

78 

79 

68.42 

39.50  68.24 

39.80!I68.0740.10 

67.89 

40.39 

79 

80 

69.26 

40.00  69.11 

40.30 

68.93  40.60 

68.75 

40.90 

80 

81 

70.15 

40.50  169.97 

40.81 

69.7941.11 

69.61 

41.41 

81 

82 

71.01 

41.00;  70.83 

41.31 

70.65  41.62 

70.47 

41.93 

82 

83 

84 

71.88 
72.75 

41.50J  71.70 
42.00|72.56 

41.81 
42.32 

71.5242.13 
72.38  42.63 

71.33 
72.19 

42.44 
42.95 

83 

84 

85 

73.61 

42.50  73.43 

42.82 

73.2443.14 

73.05 

43.46 

85 

86 

74.48 

43.00!  74.29 

43.32 

74.1043.65 

73.91 

43.97 

86 

87 

75.34 

43.50|  75.  15 

43.83 

74.96 

44.16 

74.77 

44.48 

87 

88 

76.21 

44.00i76.02 

44.33 

75.82  44.66 

75.63 

44.99 

88 

89 

77.08 

44.50:  76.88 

44.84 

76.6845.17 

76.49 

45.51 

89 

90 

77.94 

45.00|  77.75 

4o.34 

77.5545.68 

77.35 

46.02 

90 



"I 





I  



91 

78.81 

45.50  78.61 

45.84 

78.4146.19 

78.21 

46.53 

91 

92 

79.67 

46.00  79.47 

46.35 

79.2746.69 

79.07 

47.04 

92 

93 

80.54 

46.50  80.34 

46.85 

80.1347.20 

79.92 

47.55 

93 

94 

81.41 

47.00i81.20 

47.35 

80.9947.71 

80.78 

48.06 

94 

35 

82.2? 

47.50:82.06 

47.86 

31.8543.22 

81.64 

48.57 

95 

96183.14 

48.00'  82.93 

48.36 

82.7248.72 

82.50 

49.08 

96 

97184.00 

48.50:  83.79 

48.87 

83.5849.23 

83.36 

49.60 

97 

98 

84.87 

49.00:  84.66 

49.37 

84.4449.74 

84.22 

50.11 

98 

99 

85.74 

49.50  85.52 

49.87 

85.30  50.25 

85.08 

50.62 

99 

100 

86.60 

50.00,86.38 

50.38 

86.1650.75 

85.94 

51.13 

100 

CO 

Dep. 

Lat.  *  Dep. 
• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

"8 

s 

60  D*x  |59£Dog. 

59iDeg. 

59fDeg. 

Q 

100 


TRAVERSE  TABLE, 


g 

31   Deg. 

3UDeg.!3Ht)eg. 

31fDeg 

5£ 

Lat. 

Dep. 

Lat.!  Dep. 

Lat.  Dep. 

Lat. 

Dep. 

1 

0.86 

0.51 

0.85|  0.52 

0.85 

0.52 

0.85 

0.53 

2 

1.71 

1.03 

1.71    1.04 

1.71 

1.04 

1.70 

1.05 

< 

3 

2.57 

1.55 

2.56    1.56 

2.56    1.57 

2.55 

1.58 

j 

4 

3.43 

2.06 

3.421  2.08 

3.41!  2.09 

3.40 

2.10 

i 

5 

4.29 

2.58 

4.27   2.59 

,  4.26;  2.61 

4.25 

2.63 

I 

6 

5.14 

3.09 

5.13   3.  IK 

|  5.12 

3.13 

5.10 

3.16 

6 

7 

6.00 

3.61 

5.98   3.63 

5.97 

3.66 

5.95 

3.68 

', 

8 

6.86 

4.12 

6.84i  4.15 

6.82 

4.18 

6.80 

4.21 

8 

9 

7.71 

4.64 

7.69   4.67 

I  7.67 

4.70 

7.65 

4.74 

9 

10 

8.57 

5.15 

8.55   5.19 

!  8.53 

5.22 

8.M) 

5.26 

10 

11 

9.43 

5.67 

9.40   5.71 

9.38 

5.75 

9.35 

5.79 

U 

12 

10.29 

6.18  10.26   6.23|  10.23 

6.27 

10.20 

6.31 

12 

13 

11.14 

6.70  11.11    6.741  11.08 

6,79 

11.05 

6.84 

13 

14 

12.00 

7.21 

11.97,  7.26 

11.94 

7.31 

11.90 

7.37 

\i 

15 

12.86 

7.73  12.82;  7.78 

12.79 

7.84 

12.76 

7.89 

15 

16 

13.71 

8.24  13.68    8.30 

13.64 

8.36 

13.61 

8.42 

16 

17 

14.57 

8.76114.53!  8.82 

14.49 

8.88 

14.46 

8.95 

17 

18 

15.43 

9.27J15.39J  9.34 

15.35 

9.40 

15.31 

9.47 

18 

19 

16.29 

9.79i  16.24i  9.86 

16.20 

9.93 

16.16 

10.00 

19 

20 

17.14 

10.30  ill  7.  10  10.38 

17.05 

10.45 

17.01 

10.52 

20 

II 

21 

18.00 

10.82JJ  17.95  10.89 

17.91 

10.97  17.86lll.05 

21 

22 

18.86 

11.33  118.81  11.41 

18.7611.49  18.71  11.58 

22 

23 

19.7111.85 

19.66  11.93 

19.61  12.02  19.56  12.10 

23 

24 

20.57 

12.36 

20.52  12.45 

20.46 

12.54  20.41  12.63 

24 

25 

21.43 

12.88  21.37  12.97' 

21.32 

13.06  21,26  13.16 

25 

26 

22.29 

13.39'  22.23  13.49 

22.17  13.58  22.11  13.68 

26 

27 

23.14 

13.91 

23.08  14.01 

23.02 

14.11  22.9614.21 

27 

28 

24.00 

14.42 

23.94  14.53 

23.87 

14.63  23.81  14.73 

28 

29 

24.86 

14.94  24.79  15.04 

24.73  16.15  24.66  15.26 

29 

30 

25.71 

15.45  J25.65  16.56 

25.58ll5.67  25.51  15.79 

36 

31 

26.67  15.97  26.60  16.08 

26.43  16.20  26.36  16.31 

31 

32 

27.43!  16.48  27.36  16.60 

2-J.28il6.72  27.21  16.84 

32 

3328.29117.00  28.2117.12 

28.1417.24  28.0617.37 

33 

34  29.  14!  17.51  29.0717.64 

28.99  17.76  28.91  17.89 

34 

35|30.00;  18.03  29.9218.16 

29.84  18.29  29.76  18.42 

35 

36 

30.86118.54  30.7818.68 

30.70  18.81  30.61  18.94 

36 

37 

31.7219.06  31.6319.19 

31.5619.33  31.4619.47 

37 

38 

32.57  19.57  32.49  19.71 

S2.40  19.85  32.31  20.00 

38 

39 

33.4320.09  33.3420.23 

33.2520.38  33.1620.52 

39 

40 

34.29 

20.60J  34.20  20.75, 

34.11 

20.90:34.0121.05 

40 

41 

35.14 

21.12  35.0521.27 

34.96  21.42  !34.86  21.57 

41 

42 
43 

36.00 
36.86' 

21.63,35.9121.79 
22.15136.7622.31 

36.81  21.94  35.71  22.10 
36.66  22.47  |36.57  22.63 

42. 
43 

44  37.  72J22.66  37.6222.83 
4538.5723.18138.4723.34 

37.52122.99  (37.42  23.  15 
38.37  23.51  138.27  23.68 

44 
45 

46,39.43|23.69:  39.33  23.86 

39.2224.03  39.1224.21 

46 

4740.2924.21  40.1824.38 

40.0724.56  39.97  24.  73  j  47 

48 

41.14 

24.72  41.0424.90 

40.93  25.08i  40.82  25.26'  48 

49 

42.00 

25-24  41.8925.42 

41.7825.6041.6725.78    49 

50 

42.86 

25.75J  42.7525.94j'42.63!26.12  42.5226.31 

50 

J 

I 

1  _i_i  .      '--i- 



j| 

Dep. 

Lat.  Dep.  Lat. 

DepJ 

Lat.  j|  Dep.   Lat. 

-s 

5 

59  Deg.^58£Deg. 

5811 

)eg. 

58iDeg.p 

TRAVERSE  TABLE. 


101 


o 

31  Deg. 

31  ^  Deg. 

Sl^Deg. 

31£Deg. 

g 

B 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

51 

43.72 

26.27 

43.60 

26.46 

43.48 

26.65 

43.37 

26.84 

51 

52 

44.57 

26.78 

44.46 

26.98 

44.34 

27.17 

44.22 

27.36 

52 

53 

45.43 

27.30 

45.31 

27.49 

45.19 

27.69 

45.07 

27.89 

53 

54 

46.29 

27.81 

46.17 

28.01 

46.04 

28.21 

45.92 

28.42 

54 

55 

47.14 

28.33 

47.02 

28.53 

46.90 

28.74 

46.77 

28.94 

55 

56 

48.00 

28.84 

47.88 

29.05 

47.75 

29.26 

47.62 

29.47 

56 

57 

48.86 

29.36 

48.73 

29.57 

48.60 

29.78 

48.47 

29.99 

57 

58 

49.72 

29.87 

49.68 

30.09 

49.45 

30.30 

49.32 

30.52 

58 

59 

50.57 

30.39 

50.44 

30.61 

50.31 

30.83 

50.17 

31.05 

59 

60 

51.43 

30.90 

51.29 

31.13 

51.16 

31.35 

51.02 

31.57 

60 

61 

52.29 

31.42 

52.15 

31.65 

52.01 

31.87 

51.87 

32.10 

61 

62 

53.14 

31.93 

53.00 

32.16 

52.86 

32.39 

52.72 

32.63 

62 

63 

54.00 

32.45 

53.86^32.68 

53.72 

32.92 

53.57 

33.15 

63 

64 

54.86 

32.96 

54.  71  '33.20 

54.57 

33.44 

54.42 

33.68 

64 

65 

55.72 

33.48 

55.57  33.72 

55.42 

33.96 

55.27 

34.20 

65 

66 
67 

56.57 
57.43 

33.99 
34.51 

56.4234.24 
57.2834.76 

56.27 
57.13 

34.48 
35.01 

56.12 

56.98 

34.73 
35.26 

66 
67 

68 

58.29 

35.02 

58.13i35.28 

57.98 

35.53 

57.82 

35.78 

68 

69 

59.14 

35.54 

58.99135.80 

58.83 

36.05 

58.67 

36.31 

69 

70 

60.00 

36.05 

59.8436.31 

59.68 

36.57 

59,52 

36.83 

70 

71 

60.86 

36.57 

60.7036.83 

60.54 

37.10 

60.37 

37.36 

71 

72 

61.72 

37.08 

61.55i37.35 

61.39 

37.62 

61.23 

37.89 

72 

73 

62.57 

37.60 

62.41  137.  87 

62.24 

38.14 

62.08 

38.41 

73 

74 

63.43 

38.11 

63.2638.39 

63.10 

38.66 

62.93 

38.94 

74 

75 

64.29 

38.63 

64.1238.91 

63.95 

39.19 

63.78 

39.47 

75 

76 

65.14 

39.14 

64.97  39.43 

64.80 

39.71 

64.63 

39.99 

76 

77 

66.00 

39.66 

65.8339.95 

65.65 

40.23 

65.48 

40.52 

77 

78 

66.86 

40.17 

66.68140.46 

66.51 

40.75 

66.33 

41.04 

78 

79 

67.72 

40.69 

67.54  40.98 

67.36 

41.28 

67.18 

41.57 

79 

80 

68.57 

41.20 

68.39 

41.50 

68.21 

41.80 

68.03 

42.10 

80 

81 

69.43 

41.72 

69.25 

42.02 

69.06 

42.32 

68.88 

42.62 

81 

82 

70.29 

42.23 

70.10 

42.54 

69.92 

42.84 

69.73 

43.15 

82 

83 

71.14 

42.75 

70.96 

43.06 

70.77 

43.37 

70.58 

43.68 

83 

84 

72.00 

43.  2b 

71.81 

43.58 

71.62 

43.89 

71.43 

44.20 

84 

85 

72.86 

43.78 

72.67 

44.10 

72.47 

44.41 

72.28 

44.73 

85 

86 

73.72 

44.29 

73.52 

44.61 

73.33 

44.93 

73.13 

45.25 

86 

87 

74.57 

44.81 

74.38 

45.13 

74.18 

45.46 

73.98 

45.78 

87 

88 

75.43 

45.32 

75.23 

45.65 

75.03 

45.98 

74.83 

46.31 

88 

89 

76.29 

45.84 

76.09 

4o.l7 

75.88 

46.50 

75.68 

46.83 

89 

90 

77.15 

46.35 

76.94 

46.69 

76.74 

47.02 

76.53 

47.36 

90 

91 

78.00 

46.87 

77.80 

47.21 

77.59 

47.55 

77.38 

47.89 

91 

92 

78.86 

47.38 

78.65 

47.73 

78.44 

48.07 

78.23 

48.41 

92 

93 

79.72 

47.90 

79.51 

48.25 

78.30 

48.59 

79.0 

48.94 

93 

94180.57 

48.41 

80.36 

4b.76 

80.15 

49.11 

79.93 

49.47 

94 

95 

81.43 

48.93 

81.22 

49.28? 

81.00 

49.64 

80.7 

49.99 

95 

96 

82.29 

49.44 

82.07 

49.80 

81-85 

50.16 

81.63 

50.52 

96 

97 

83.15 

49.96 

82.93 

50.32 

82.71 

50.68 

82.48 

51.04 

97 

98 

84.00 

50.47 

83.78 

50.84 

83.56 

51.20 

83.33 

51.57 

98 

99 

84.86 

50.99 

84.64 

51.36 

84.41 

51.73 

84.18 

52.10 

99 

100 

85.72 

51.50 

85.49 

51.88 

85.26 

52.25 

85.04 

52.62 

100 

3 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

Lat 

Dep 

Lat. 

•£ 

en 

CO 

5 

59  Deg. 

58|De?i. 

58iDeg 

58-fDeii. 

5 

102 


TRAVERSE  TABLE, 


g 

32  Deg. 

32fl)eg. 

32£Deg. 

32$  Dei'. 

« 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

K 

1 

0.85 

0.53 

0.85 

0.53 

0.84 

0.54 

0.84 

0.54 

i 

2 

1,70 

1.06 

1.69 

1.07 

1.69 

1.07 

1.68 

1.08 

2 

3 

2.54 

1.59 

2.54 

1.60 

2.53 

1.61 

2.52 

1.62 

3 

4 

3.39 

2.12 

3.38 

2.13 

3.37 

2.15 

3.36 

2.16 

4 

5 

4.24 

2.65 

4.23 

2.67 

4.22 

2.69 

4.21 

2.70 

I 

6 

5.09 

3.18 

5.07 

3.20 

5.06 

3.22 

5.05 

3.25 

6 

7 

5.94 

3.71 

5.92 

3.74 

5.90 

3.76 

5.89 

3.79 

7 

8 

6.78 

4.24 

6.77 

4.27  1 

6.75 

4.30 

6.73 

4.33 

8 

9 

7.63 

4.77 

7.61 

4.80 

7.59 

4.84 

7.57 

4.87 

9 

10 

8.48 

5.30 

8.46 

5.34 

8.43 

6.37 

8.41 

5.41 

10 

11 

9.33 

6.83 

9.30 

5.87 

9.28 

5.91 

9.25 

5.95 

11 

12 

10.18 

6.36 

10.15 

6.40 

10.12 

6.45 

10.09 

6.49 

12 

13 

11.02 

6.89 

10.98 

6.94 

10.96 

6.98 

10.93 

7.03 

13 

14 

11.87 

7.42 

11.84 

7.47 

11.81 

7.52 

11.77 

7.57 

14 

15 

12.72 

7.95 

12.69 

8.00 

12.65 

8.06 

12.62 

8.11 

15 

16 

13.57 

8.48 

13.53 

8.54 

13.49 

8.60 

13.46 

8.6S 

16 

17 

14.42 

9,01 

14.38 

9.07 

14.34 

9.13 

14.30 

9.20 

17 

18 

15.26 

9.54 

15.22 

9.61 

15.18 

9.67 

15.14 

9.74 

18 

19 

16.11 

10.07 

16.07 

10.14 

16.02 

10.21 

15.98 

10.28 

19 

20 

16.96 

10.60 

16.91 

10.67 

16.87 

10.75 

16.82 

10.82 

20 

21 

17.81 

11.13 

17.76 

11.21 

17.71 

11.28 

17.66 

11.36 

21 

22 

18.66 

11.66 

18.61 

11.74 

18.55 

11.82 

18.50 

11.90 

22 

23 

19.51 

12.19 

19.45 

12.27 

19.40 

12.36 

19.34 

12.44 

23 

24 

20.35 

12.72 

20.30 

12.81 

20.24 

12.90 

20.18 

12.98 

24 

25 

21.20 

13.25 

21.14 

13.34 

21.08 

13.43 

21.03 

13.52 

25 

26 

22.05 

13.78 

21.99 

13.8- 

21.93 

13.97 

21.8V 

14,07 

26 

27 

22.90 

14.31 

22.83 

14.41 

22.77 

14.51 

22.71 

14.61 

27 

28 

23.75 

14.84 

23.68 

14.94 

23.61 

15.04 

23.55 

15.15 

28 

29 

24.59 

15.37 

24.53 

15.47 

24,46 

15.58 

24.39 

15.69 

29 

30 

25.44 

15.90 

25.37 

16.01 

25.30 

16.12 

25.23 

16.23 

30 

31 

26.29 

16.43 

26.22 

16.54 

26.1o 

16.66 

26.07 

16.77 

31 

32 

27.14 

16.96 

27.06 

17.08 

26.99 

17.19 

26.91 

17.31   32 

33,27.99 

17.49 

27.9 

17.61 

27.83 

17.73 

27.75 

17.85 

33 

34128.83 

18.02 

28.75 

18.14 

28.68 

18.27 

28.60 

18.39 

34 

35  29.68 

18.55 

29.60 

18.68 

29.52 

18.8 

29.44 

18.93 

35 

3690,68 

19.08 

30.45 

19.21 

30.36 

19.34 

30.28 

19.48 

36 

3731.38 

19.61 

31.2 

19.74 

31.2 

19.88 

31.12 

20.02J  37 

3832.23 

20.14 

32.14 

20.28 

32.05 

20.42 

31.96 

20.56!  38 

3933.07 

20.671  32.9 

20.8 

32.89 

20.95 

32.80 

21.10:  39 

40 

[33.92 

21.20  33.83 

21.34 

33.74 

21.49 

33.64 

21.64 

40 

41 

34.7 

21.73  34.6 

21.88 

34.5 

22.03 

34.48 

22.18 

41 

42,35.62 

22.26 

35.5 

22.4 

35.42 

22.5 

35.32 

22.72 

42 

43,36.4 

22.79 

36.3 

22.95 

36.2 

23.1 

36.16 

23.26 

43 

44137.3 

23.S2 

37.2 

23.4 

37.1 

23.6 

37.0 

23.  8C 

44 

45138.1 

23.85 

38.0 

24.0 

37.9 

24.1 

37.85l24.34 

45 

4(3 

39.0 

24.38 

38.9 

24.55 

38.8C 

24.7 

38.69(24.88 

46 

4' 

39.8 

24.91 

39.7 

25.08 

39.64 

25.2 

39.53J25.43 

47 

4t 

40.7 

25.44 

40.5 

25.61 

40.4 

25.7 

40.37 

25.97 

48 

4£ 

41.5 

>42.4C 

25.97 
26.50 

41.4 

42.2 

26.15 
26.68 

41.3 
42.1 

26.3 
26.8 

41.21 

42.05 

26.51 
27.05 

49 
50 

to 

Dep 

Lat. 

Dep 

Lat. 

Dep 

Lat 

Dep. 

Lat. 

CO 

QJ58   Dag. 

!57fDeg. 

57£D<^ 

67;  Deg. 

o 

TRAVERSE  TABLE. 


103 


o 

32  Peg. 

32i£)eg. 

32i  Deg. 

32£Deg. 

d 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Oep. 

Lat.  Dep. 

r 

,51 

43.25 

27.03 

43.13 

27.21 

43.01 

7.40  42.89'27.59 

51 

52 

44.10 

27.56 

43.98 

27.75 

3.86 

7.94i,43.7328.13 

52 

53 

4.95 

28.09 

44.82 

28.28 

4.70 

8.48 

44.58  28.67 

53 

54 

5.79 

28.62 

45.67 

28.82 

5.54 

9.01| 

45.4229.21 

54 

55 

6.64 

29.15 

46.51 

29.35 

6.39 

9.55 

46.2629.75 

55 

56 
57 

7.49 
8.34 

29.68 
30.21 

47.36 
48.21 

29.88 
30.42 

7.23 
8.07 

30.09147.10:30.29 
0.63!  47.94130.84 

56 
57 

58 

9.19 

30.74 

49.05 

30.95 

8.92 

1.16 

48.78  31.38 

58 

59 

50.03 

31.27 

49.90 

31.48 

9.76 

1.70 

49.6231.92 

59 

60 

50.88 

31.80 

50.74 

32.02 

0.60 

2.24 

50.46JS 

J2.46 

60 

fil 

1.73 

12.33 

51.59 

12.55 

1.45 

2.78 

51.30  £ 

J3.00 

61 

62 

2.58 

32.85 

52.44 

33.08 

2.29 

33.31 

52.14^3.54 

62 

63 

3.43 

33-.  38 

53.28 

33.62 

3.13 

3.85 

52.99  34.08 

63 

64 

4.28 

33.91 

54.13 

34.15 

3.98 

4.39 

53.83134.62 

64 

65 

5.12 

34.44 

54.97 

34.68 

4.82 

4.92: 

54.6735,16 

65 

66 

55.97 

34.97 

55.82 

35.22 

55.66 

5.46 

55.51  ' 

35.70 

66 

67 

o6.82 

35.50 

56.66 

35.75 

56.51 

6.00 

56.35 

36.25 

67 

68 

57.67 

36.03 

57.51 

36.29 

57.35 

6.54! 

57.19i36.79 

68 

69 

58.52J36.56 

58.36 

36.82 

58.19 

7.07 

58.03i37.33 

69 

70 

59.36^7.09 

59.20 

37,35 

59.04 

7.61 

58.87:37.87 

70 

71 

60.21  !37.62 

0.05 

37.89 

59.88 

38.15 

59.71:38.41 

71 

72 

61.0638.15 

0.89 

38.42 

60.72 

38.69 

60.5538.95 

72 

73 

61.91  38.68 

1.74 

38.95 

61.57 

39.221 

61.40  39.49 

73 

74 

62.7639.21 

2.58 

39.49 

62.41 

39.76 

62.2440.03 

74 

75 

63.6039.74 

63.43 

40.02 

63.25 

40.30 

63.08  40.57 

75 

76 

64.45;40.27 

54.28 

40.55 

54.10 

;0.83 

63.9241.11 

76 

77 

65.3040.80 

65.12 

41.09 

64.94 

41.37 

64.7641.65 

77 

78 

66.1541.33 

65.97 

41.62 

65.78 

41.91 

65.60'42.20 

78 

79 

67.0041.86 

66.81 

42.16 

66.63 

42.45 

66.44J42.74 

79 

80 

67.8442.39 

67.66 

42.69 

67.47 

42.98  67.2843.28 

80 

81 

68.6942.92 

68.50  43.22 

68.31 

43.59, 

J68.  12  43.82 

81 

82 
83 

69.5443.45 
70.39  43.98 

69.35 

70.20 

43.76 
44.29 

69.16 
70.00 

44.06 
44.60 

68.9744.36 
69.81  !44.90 

82 
83 

84 

85 

71.2444.51 
72.08  45.04 

71.04 
71.89 

44.82 
45.36 

70.84 
71.69 

45.13 
45.67 

70.6545.44 
71.4945.98 

84 
85 

86 

72.9345.57 

72.73 

45.89 

72.53 

46.21 

72.33  46.52 

86 

87 

73.7846.10 

73.58 

46.42 

73.38 

46.75 

73.1747.06 

87 

88 

74.63(46,63 

74.42 

46.96 

74.22 

47.28  ^74.01  47.61 

88 

89 

75.4847.16 

75.27 

47.49 

75.06 

47.82  74.85:43.15 

89 

90 

76.32 

47.69 

76.12 

48.03 

75.9 

48.36  75.69 

48.69 

90 

9 

77.17 

48.22 

76.96 

48.5 

76.75 

48.89 

76.53 

49.23 

91 

92 

78.02l48.75 

77.81 

49.09 

77.59 

49.43 

77.38 

49.77 

92 

93 

78.8749.28 

78.65 

49.63 

78.4 

49.97 

78.22 

50.31 

93 

94 
9, 

79.7249.81 
80.5650.34 

79.50 
80.34 

50.1 
50.6 

79.2 
80.12 

50.51 
51.04 

79.06 
79.90 

50.85 
ftl.JW 

94 
95 

9fi 

81.4150.87 

81.19 

51.2 

80.9 

51.58 

80.74 

51.93 

96 

9 

82.2651.40 

82.04 

51.7 

81.8 

52.12 

81.58 

52.47 

97 

9 

S3.1l|51.& 

82.86 

52.2J 

82,6 

52.66J  J82.42 

53.02 

98 

9 

ia 

83.9* 

84.  8( 

552.46 
)  52.99 

83.  7£ 
84.5' 

52.8 
53.3 

83.50 
84.3 

53.19  83.26 
53.73H84.10 

53.56 
54.  1C 

99 
100 

X 

Dep 

Lat 

Dep. 

Lat 

Dep 

Lat. 

Dep.l  Lat. 

as 

58    Peg 

57£Deg 

57iDeg. 

57fDeg 

/•«i 

104 


TRAVERSE  TABLE. 


0 

33  Deg. 

33iDeg. 

33iDeg. 

83|Deg.(O 

p." 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

1 

0.84 

0.54 

0.84 

0.55 

0.83 

0.55 

!  0.83 

0.56 

i 

2 

1.68 

1.09 

1.67 

1.10 

1.67 

1.10 

i    1.66 

1.11 

2 

3 

2.52 

1.63 

2.51 

1.64 

2.50 

1.66 

2.49 

1.67 

3 

4 

3.35 

2.18 

3.35 

2.19 

3.34 

2.21 

3.33 

2.22 

4 

5 

4.19 

2.72 

4.18 

2.74 

4.17 

2.76 

4.16 

2.78 

5 

6 

6.03 

3.27 

5.02 

3.29 

5.00 

3.31 

4.99 

3.33 

6 

7 

5.87 

3.811 

5.85 

3.84 

6.84 

3.86 

5.82 

3.89 

7 

8 

6.71 

4.33    6.69 

4.39 

6.67 

4.42 

6.65 

4.44 

8 

9 

7.55 

4.90    7.53 

4.93 

7.50 

4.97 

i  7.48 

5.00 

9 

10 

8.39 

5.45    8.36 

5.48 

8.34 

5.52 

8.31 

5.56 

10 

11 

9.23 

5.99 

9.20 

6.03 

9.17 

6.07 

9.15 

6.11 

11 

12 

10.06 

6.54 

10.04 

6.59 

10.01 

6.62 

9.98 

6.67    12 

13 

10.90 

7.08 

10.87 

7.13 

10.84 

7.18 

10.81 

7.22J  13 

14 

11.74 

7.62: 

11.71 

7.68 

11.67 

7.73 

11.64 

7.781   14 

16J12.58 

8.17 

12.64 

8.22 

12.51 

8.28 

12.47 

8.33    15 

1613.42 

8.71 

13.38 

8.77 

13.34 

8.83 

13.30 

8.89    19 

17  14.26 

9.26 

14.22 

9.32 

14.18 

9.38 

14.13 

9.441  17 

1815.10 

9.80 

15.05 

9.87 

15.01 

9.93  114.97 

10.00   18 

19;  15.93 

10.35 

15.89 

10.42 

15.84 

10.49 

15.80 

10.56    19 

2016.77 

10.89 

16.73 

10.97 

16.68 

11.04 

16.63 

11.11 

20 

2li  17.61 

11.44 

17.56 

11.51 

17.51 

11.59 

17.46 

11.67 

21 

22|  18.45  11.  98 

18.40  12.06 

18.35 

12.14 

18.29 

12.22 

22 

23  19.29  12.63 

19.23  12.61 

19.18 

12.69 

19.12 

12.78 

23 

2420.1313.07 

20.0713.16 

20.01 

13.25 

19.96 

13.33 

24 

25:20.97  13.62  20.91  13.71 

20.85 

13.80 

20.79 

13.89 

25 

26  21.81  14.16  121.74  14.26 

21.68 

14.35 

21.62 

14.44 

26 

27  22.64  14.71;  22.58  14.  80 

22.51 

14.90 

22.45 

15.00 

27 

28!23.48  15.25!  23.42  15.35 

23.35 

15.45 

23.28 

15.56 

28 

29:24.32  15.79 

24.25  15.90 

24.18 

16.01 

24.11 

16.11 

29 

3025.16 

16.34 

25.0916.45 

25.02 

16.56 

24.94 

16.67 

30 

31  26.00  16.88 

25.92  17.00 

25.85 

17.11 

25.78 

17.22'  31 

32  26.84  17.43  126.76  17.55 

26.68 

17.66 

26.61 

17.78!  32 

33  27.68  17.971 

27.60  18.09 

27.52 

18.21 

27.44 

18.33 

33 

34  28,51  18.521 
3529.3519.06! 

28.43  18.64 
29.2719.19 

28.35 
29.19 

18.77 
19.32 

28.27 
29.10 

18.89 
19.44 

34 
35 

3630.19 

19.61  30.  11  19.74 

30.02 

19.87 

29.93 

20.00!  36 

37  31.03  20.15  130.94  20.29  30.85 

20.42 

30.76 

20.56   37 

38i31.87j20.70t!31.78  20.84  ;31.69 

20.97 

31.60 

21.111  38 

39 

32.71  21.24  132.62  21.38  32.52 

21.53 

32.43 

21.671  39 

40  33.55 

21.79  33.45  21.93;  |33.S6 

22.08 

33.26 

22.221  40 

4134.39 

22.33  34.29^2.48134.19 

22.63 

34.09 

22.78   41 

4235.22 

22.87  35.  12i23.03l  36.02 

23.18  34.92 

23.33  42 

4336.06 

26.42 

35.96'23.58 

35.86 

23.73  35.75 

23.89   43 

44 

36.90 

23.96; 

36.8024.12 

36.69 

24.29 

36.58 

24.45!  44 

4537.74 

24.51 

37.63  24.67!  137.52 

24.84 

37.42 

25.00   45 

4638.58 

25.05!  38.47  25.22  38.36 

25.39 

38.25 

25.56;  46 

47  39.42 

25.60  39.31125.77 

39.19 

25.94 

39.08 

26.11 

47 

4840.26 

26.14 

40.1426.32 

40.03 

26.49 

39.91 

26.67 

48 

4941.09 

26.69 

40.98!26.87 

40.86 

27.04 

40.74 

27.22 

49 

50 

41.93 

27.23 

41.81  27.41 

41.69 

27.60 

41.57 

27.78 

50 

D^pT 

Lat. 

Dep.l  Lat. 

^j 

Dep. 

Lat. 

Dep. 

Lat. 

-»j 

CO 

- 

p 

57  Deg. 

|56peg. 

56jDeg. 

56iDeg.  Q 

TRAVERSE  TABLE. 


Wti 


g 

33  Deg. 

33£Deg. 

33£Deg. 

33|  Deg. 

o 

n-» 

r' 

Lat.|Dep. 

Lat.lDep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

51 

42.7727.78 

42.6527.96 

42.53 

28.15 

42.40 

28.33   51 

52 
53 

43.6128.32 
44.45:28.87 

43.4928.51  43.36 
44.3229.06144.20 

28.70  43.24 
29.25  44.07 

28.89 
29.45 

52 
53 

54 
55 
56 

45.29  29.41 
46.1329.96 
46.97  30.50 

45.16i29.6l  45.0329.80 
46.00;30.16|I45.86I30.36 
46.83l30.70i46.70j30.91 

44.90 
45.73 
46.56 

30.00J  54 
30.56   55 
31.11    56 

57  47.80j31.04 

7.67|31.25S  47.53  31.46 

47.3931.67]  57 

5848.6431.59 

8.50  31.  80'  '48.37  32.01 

48.2332.22   58 

5949.48i32.13 

9.34'32.35i  49.20  32.56 

49.0632.78 

59 

6050.32 

32.68 

Q.  18^32.901  50.03  33.  12 

49.89  33.33 

60 

6151.16 

33.22 

1.01  '33.45  '50.87  33.67 

50.72l33.89   61 

6252.0033.77 

1.8533.99^51.7034.22 

51.5534.45!  62 

6352.8434.31 

2.69!34.54  52.53  34.77 

52.3835.00   63 

64:53.67  34.86 

3.52'35.09:  53.37  35.32 

53.2135.56 

64 

65!54.51  35.40 

4.36J35.64  !54.20'35.88 

54.0536.11 

65 

66  55.35  35.95 

5.19136.19  55.04l36.43 

54.8836.67 

66 

6756.1936.49 

56.03l36.74ii55.87  36.98 

55.71  37.22 

67 

6857.0337.04 

6.87^37.28  56.7037.53 

56.5437.78 

68 

69  57.87  37.58 

7.7037.83  57.5438.08 

57.37  38.33 

69 

7058.71:38.12 

58.54:38.38  58.37  38.64 

58.2038.89 

70 

| 

______ 

I 

_____ 

_ 



_ 



7159.5538.67 

9.3838.93  59.2139.19 

59.0339.45 

71 

72  60.38  39.21 

60.21  39.481  60.04  39.74 

59.87  40.00 

72 

7361.2239.76 

61.05  40.03  60.87  40.29 

60.70  40.56 

73 

74J62.06  40.30 

61.89  40.57  61.71  40.84 

61.5341.11 

74 

7562.9040.85 

62.7241.12  62.5441.40 

62.3641.67 

75 

7663.7441.39 

63.5641.67  63.3841.95 

63.1942.22 

76 

77|64.5841.94 

64.39  42.22J  64.21  42.50 

64.02  42.78 

77 

78  65.42  42.48 

65.2342.77  65.0443.05 

64.8543.33 

78 

7966.2543.03 

66.07  43.32  65.88  43.60 

65.69  43.89 

79 

80  67.09143.57 

66.9043.86  66.7144.15 

66.5244.45 

80 

8167.9344.12 

67.74  44.4ll  67.54  44.71 

67.3545.00 

81 

8268.77i44.66 

68.58  44.96  68.38  45.26 

68.1845.56 

82 

83:69.61  45.20 

69.41  45.51  69.21  45.81 

69.0146.11 

83 

84j70.45  45.75 
8571.2946.29 

70.25  46.06  70.05  46.36 
71.08  46.60li70.88  46.91 

69.8446.67 
70.67  47.22 

84 
85 

86l72.13.46.84 

71.92  47.15jl71.71  47.47 

71.5147.78 

86 

87  72.96 

47.38 

72.7647.70  72.5548.02 

72.3448.83 

87 

88 

73.80 

47.93 

73.59  48.26 

73.38]48.57 

73.1748.89 

88 

89 

74.64 

48.47 

74.43  48.80 

74.22 

49.12 

74.00 

49.45 

89 

90 

75.48 

49.02 

75.27  49.35 

75.05 

49.67 

74.83 

50.00   90 

91 

76.32 

49.56 

76.1049.89 

75.88 

50.23 

75.66 

50.56   91 

92 

77.16 

50.11 

76.94  50.44 

76.72|50.78:i76.5051.11 

92 

93 

78.00 

50.65 

77.77  50.99 

77.5551.33 

77.3351.67 

93 

94 
95 
96 
97 

78.8351.20 
79.6751.74 
80.5152.29 

81.3552.83 

78.61  51.54 
79.45  52.09 
80.28  52.64 
81.1253.18 

78.39  51.  88  i78.  16 
79.22  52.43  |78.99 
!80.0552.99J  79.82 
80.89  53.54  J80.65 

[52.22 
'52.78 
'53.33 
53.89 

94 
95 
96 
97 

98 

82.  19153.37 

81.9653.73 

'81.72 

54.09  181.48 

54.45 

98 

99 
100 

83.03 
83.87 

53.92 
54.46 

'82.79  64.28 
83.63  64.83 

82.55 
83.39 

54.64 
55.19 

182.32 
83.15 

55.00 
55.56 

99 
100 

^ 

Dep. 

Lat 

Dep.  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

ts 

s 

57 

Deg 

56£Deg.!'56' 

Deg. 

56£Deg.i5 

TRAVERSE  TABLE. 


g 

34  Deg. 

34fDeg. 

34^  Deg. 

34^  Deg. 

0 

K 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

i 

0.83 

0.56 

0.83 

0.56 

0.32 

0.57 

0.82 

0.57 

i 

2 

1.66 

L12 

1.65 

1.13 

1.65 

1.13 

1.64 

1.14 

2 

3 

2.49 

1.68 

2.48 

1.69 

2.47 

1.70 

2.46 

1.71 

S 

4 

3.32 

2.24 

3.31 

2.25 

3.30 

2.27 

3.29 

2.28 

4 

5 

4.15 

2.80 

4.13 

2.81 

4.12 

2.83 

4.11 

2.85 

5 

6 

4.97 

3.36 

4.96 

3.38 

4.94 

3.40 

4.93 

3.42 

6 

7 

5.80 

3.91 

5.79 

3.94 

5.77 

3.96 

5.75i  3.99 

7 

8 

6.63 

4.47 

6.61 

4.50 

6.59 

4.53 

6.57 

4.56 

8 

9 

7.46 

5.03 

7.44 

5.07 

7.42 

5.10 

7.39 

5.13 

9 

10 

8.29 

5.59 

8.27 

5.63 

8.24 

5.66 

8.22 

5.70 

10 

11 

9.12 

6.15 

9.09 

6.19 

9.07 

6.23 

9.04 

6.27 

11 

12 

9.95 

6.71 

9.92 

6.75 

9.89 

6.80 

9.86 

6.84   12 

13  10.78 

7.27 

10.75 

7.32 

10.71 

7.36 

10.68 

7.41    13 

1411.61 

7.83 

11.57 

7.88 

11.54 

7.93 

11.60 

7.98   14 

15 

12.44!  8.39 

12.40 

8.44 

12.36 

8.50 

12.32 

8.55   15 

1613.26 

8.95 

13.23 

9.00 

13.19 

9.06 

13.15   9.12!  16 

17 

14.09 

9.51 

14.05 

9.57 

14.01 

9.63 

13.97 

9.69 

17 

18;  14.92  10.07 

14.88 

10.13 

14.83 

10.20 

14.79  10.26 

18 

1915.7510,62 

15.7lilO.69 

15.66  10.76 

15.61 

10.83 

19 

2016.5811.18 

16.53J  11.26 

16.48 

11.33 

16.43  11.40 

20 

21 

17.41 

11.74 

17.36111.82 

17.31  11.89 

17.2511.97   21 

22  18.24i  12.30 

18.1812.38 

18.1312.46 

18.08  12.541  22 

23 

19.07  12.86 

19.01 

12.94 

18.9513.03 

18.9013.11   23 

24 

19.90  13.42 

119.84,13.51 

19.78  13.59 

19.7213.68   24 

25J20.73  13.98 

20.66j  14.07 

20.6014.16 

20.5414.25   25 

2621.5514.54 

21.49  14.63 

21.4314.73 

21.36  14.82 

26 

27^2.3815.10:22.3215.20 

22.2515.29 

22.1815.39 

27 

28  23.21 

15.66  23.1415.76 

23.08'  15.86 

23.01 

15.96   28 

2924.0416.22 

23.97  16.32 

23.90,16.43 

23.83  16.53:  29 

3024.8716.78 

24.80;  16.88 

24.72|16.99 

24.65  17.  10|  30 

31  25.70  17.33 

25.6217.45 

25.5517.56 

25.47  17.67 

31 

32 

26.5S 

17.891  126.45  18.01 

26.3718.12 

26.2918.24  32 

33  27.36,  18.45Ji27.28  18.57 

27.2018.  69 

27.1118.81 

33 

34  28.  19;  19.011  128.1019.  14 

28.0219.26 

27.94  19.38 

34 

3529.0219.57  28.93!  W.  70 
36  29.  85  20.  13  129.  76120.26 
37  30.67  20.69  30.58  20.82 

28.84  19.82 
29.67  20.39 
30.4920.96 

28.76  19.951  35 
29.5820.52   36 
30.4021.09!  37 

38i31.50  21.25  31.4121.39 

31.3221.52 

31.22  21.66!  38 

39 
40 

32.33  21.81 
33.1622.37 

32.2421.95 
i33.0622.51 

32.1422.09 
32.97  22.66 

132.04  22.23   39 
32.8722.80  40 

41 
42 

33.99  22.93  33.89  23.07 
34.82  23.491  134.  72  23.  64 

33.7923.22 
34.61  23.79 

33.6923.37!  41 
34.5123.94   42 

43 

35.65  24.05  35.54i24.2G 

35.4424.36 

35.3324.51    43 

44  36.48  24.60  !36.37  24.76 

36.26  24.92 

36.1525.08;  44 

4537.3125.16  37.2025.33 

37.09  25.49 

'36.9725.651  45 

4638.1425.72 

38.0225.89 

37.91  26.05 

37.8026.22   46 

47  38.96  26.28  :38.85  26.45 

38.7326.62 

38.6226.79!  47 

48  39.79  26.84i  ;39.68  27.01 

39.5627.19 

39.44  27.36 

48 

49  40.62  27.401  40.50  27.58 

40.38  27.75 

40.26  27.93 

49 

50 

41.4527.96  41.3328.14 

41.21  28.32 

41.08  28.50 

50 

-4-i 

cn 

Dep.l  Lat. 

Dep.  Lat. 

Dep.  Lat. 

Dep 

Lat. 

-*-* 
.22 

5 

56 

Deg. 

553  Deg. 

55^  Deg. 

55|Deg. 

a 

TRAVERSE  TABLE,                 f  Q7 

0 

34  Deg.  34jDeg.  34fDeg.| 

34'Deg. 

g 

GO 

Lat. 

Dep.  |  Lat. 

Dep.    Lat. 

Dep. 

Lat.  Dep. 

5S* 

51 

42.28 

28.52  42.16 

28.70!  42.03 

28.89 

41.9029.07 

51 

5243.11 

29.08  42.98 

29.27!  42.85 

29.45 

42!73  29.64 

52 

53  43.94 

29.64  43.81 

29.83'  43.68 

30.02 

43.55  30.21 

53 

5444.77 

30.20  44.64 

30.39  44.50 

30.59 

44.37  30.78 

54 

55  45.60 

30.76  45.46 

30.95  45.33 

31.15 

45.1931.35 

55 

56|46.43 

31.31  46.29 

S1.52  46.1531.72 

46.01  31.92 

56 

57  47.26 

31.87  47.12 

32.08  46.98132.29 

46.8332.49 

57 

58  48.08 

32.43  47.94 

32.64  147.80  32.85 

47.66  33.06 

58 

59  48.91 

32.99  48.77 

33.21  48.6233.42 

48.4833.63 

59 

6049.74 

33.55  49.60 

33.77  49.45 

33.98 

49.3034.20 

60 

61 

50.57 

34.11  50.42 

34.33  '50.27 

34.55 

50.1234.77 

61 

62 

51.40 

34.67  51.25 

34.89!  51.  10  35.12  50.9435.34   62 

6352.23 

35.23  52.08 

35.46  51.9235,68  |51.76  35.91 

63 

64j  53.06 
65  53.89 
66  54.72 

35.79  52.90 
36.35  ,53.73 
36.91  54.55 

36.02  52.74j36.25  52.59  36.48 
36.58  53.57  36,82  53.41  37.05 
37.15  54.39^37.38  J54.23  37.62 

64 
65 
66 

67  j  55.  55 

37.46  55.38 

37.71  55.2237.95 

55.0538.19 

67 

68  56.37 

38.03  56.21 

38,27156.0438.52 

55.87  38.76 

68 

69:57.20 

38.58  57.03 

38.83  56.86  39.08 

56.69  39.33 

69 

70  58.03 

39.14  57.86 

39.40  57.69 

39.65 

57.52;39.90 

70 

7l'58.86 

39.70  58.69 

39.96  58.51 

40.21 

58.3440.47 

71 

7259.69 

40.26  59.51 

40.52  59.34 

40.78 

59.1641.04 

72 

73  60.52 

40.82  60.34 

41.08.60.16 

41.35  159.98  41.  61 

73 

74  61.35 

41.38  61.17 

41.65  60.99 

41.91  160.80  42.  18 

74 

7562.1841.94  61.99 

42.21  61.81 

42.48  |6L  62  42.75 

75 

76  63.01 
77  63.84 

42.50  62.82 
43.06  63.65 

42.77  62.63  43.05  162.45  43.32    76 
43.34  63.46i43.61  63.27  43.89    77 

78  64.66  43.62;  64.47 

43.90  64.28  44.181  64.09  44.46 

78 

79  65.49 

44.18  !65.30 

44.46  65.11144.75  64.9145.03   79 

8066.32 

44.74  66.13 

45.02j  65.93J45.31 

!65.73  45.60 

80 

8167.15 

45.29  66.95 

,  
45.59:66.7545.88  66.5546.17 

81 

82 

67.98 

45.85  67.78 

46.15  67.58146.45  67.3746.74 

82 

83  68.81 

46.41  68.61 

46.711  68.40 

47.01  68.2047,31    83 

84  69.64i46.97  169.43 

47.28  69.23  47.58'  69.02  47.88   84 

85  70.47  47.53;  70.26 

47.84  70.0548.14  69.8448.45   85 

86  71.30  48.09  !71.09 

48.40  70.87i48.71  70.6649.02 

86 

8772.1348.65  71.91 

48.96:71.70149.28  71.4849.59 

87 

8872.9649.21  72.74 

49.53  72.5249.84  72.3050.16 

88 

89  73.78i49.77  73.57 

50.09  73.35  50.41 

73.1350.73 

89 

9074.61150.33  74.39 

I  j  

50.65  74.17  50.98]  73.9551.30 

90 

91  75.44l50.89  75.22 

51.221  75.00  51.54!  74.7751.87 

91 

92  76.27151.  45  76.05 

51.78  75.8252.11  75.5952.44 

92 

9377.1052.00  76.87 

52.34  76.64  52.68  76.41  53.01 

93 

94  77.93  52.56  77.70 

52.90  77.47  53.24,  77.23  53.58 

94 

95  78.76  53.12  78.53  53.47  78.29  53.81'  78.06  54.15 

95 

96  79.59!53.68  79.35 

54.0379.1254.3778.8854.72   96 

9780.4254.24  80.18 

54.59  79.9454.94  79.  70  55.291  97 

9881.2554.80  81.01 

55.15  80.76  55.51  80.52  55.86 

98 

99  82.07  55.36  81.83 

55.72  81.59  56.071  81.34  56.43 

Q 

100^2.90,55.92  82.66 

56.28  82.41  56.64 

82.16  57.00  100 

•s 

jDep.i  Lat.  Dep. 

Lat.lDep.   Lat. 

!Dep-!kat.~ 

•  Ml 

56   Deg.  55fDeg.  55]Deg.  55jDeg.j3 

108 


TRAVERSE  TABLE. 


g 
p 

35  1 
Lai? 

Deg. 
Dep. 

35^1 

Lat. 

-Jeg. 

D^pT 

35±Deg,353Deg. 

* 

Lat. 

Dep. 

Lat.  Dep. 

I 

0.82 

0.57 

0.82 

0.58 

0.81 

0.58 

0.81 

0.58 

1 

2 

1.64 

1.15 

1.63 

1.15 

1.63 

1.16 

1.62 

1.17 

2 

3 

2.46 

1.72 

2.45 

1.73 

2.44 

1,74 

2.43 

1.75 

3 

4 

3.28 

2.29 

3.27 

2.31 

3.26 

2.32 

3.25 

2.34 

4 

5 

4.10 

2.87 

4.08 

2.89 

4.07 

2.90 

4.06 

2.92 

5 

6 

4.91 

3.44 

4.90 

3.46 

4.88 

3.48 

4.87 

3.51 

6 

7 

5.73 

4.01 

5.72 

4.04 

5.70 

4.06 

5.68 

4.09 

7 

8 

6.55 

4.59 

6.53 

4.62 

6.51 

4.66 

6.49 

4.67 

8 

9 

7.37 

5.16 

7.35 

5.19 

7.33 

5.23 

7.30 

5.26 

9 

10 

8.19 

5.74 

8.17 

5.77 

8.14   5.81 

8.12 

5.84 

10 

11   9.01 

6.31 

8.98 

6.35 

8.96   6.39 

8.93 

6.43 

11 

12  9.83 

6.88 

9.80 

6.93 

9.77   6.97 

9.74 

7.01 

12 

13  10.65 

7.46 

10.62 

7.50 

10.58 

7.55 

10.55 

7.60 

13 

1411.47 

8.03 

11.43 

8.08 

11.40!  8.13 

11.36 

8.18 

14 

15  12.29   8.60 

12.25 

8.66!  12.21 

8.71 

12.17 

8.76 

15 

1613.ll!  9.18 

13.07   9.23  13.03 

9.29 

12.99 

9.35i  16 

17 

13.93!  9.75 

13.88:  9.81  13.84   9.87 

13.80 

9.93 

17 

18 

14.74  10.32  14.70  10.39  14.65  10.45 

14.61 

10.52 

18 

19  15.56  10.90 

15.52  10.97  15.47  11.03 

15.42 

11.10 

19 

2016.3811.47 

16.33  11.54 

16.2811.61 

16.23 

11.68 

20 

21  17.20  12.05 

22  18.02  12.62; 
2318.8413.19 

24  19.66  13.77 

25  20.48  14.34| 
2621.3014.91' 

27  22. 12  15.49 

28  22.94  16.06 

29  23.76  16.63 

30  24.57  17.21 


17.1512.12 
17.97  12.70; 
18.78  13.27 
19.60  13.85 
20.42  14.43 
21.2315.01 
22.0515.58 
22.87  16.16| 
23.68  16.74, 
24.50  17.3J 


17.1012.19  17.0412.27  21 

17.91  12.78  il7.85!l2.85|  22 

,18.7213.36  18.67  i  13. 44  23 

19.5413.94  19.4814.02!  24 

20.35  14.52  20.29  14.61  25 

21.1715.10!21.10|15.19  26 

21.98  15.68  21.9l!l5. 77  27 

22.80  16.26 '22.72  16.36'  28 

23.61  16.84  |23.54|16.94  29 

24.42  17.42  24.35  17.53  30 


31  25.39  17.78  25.32  17.89  25.24  18.00  !25.16il8.11  31 

32  26.21  18.35!  26.13  18.47  26.05  18.58  25.97  18.70  32 
3327.03  18.93  26.95  19.05  26,87  19.16  26.78J19.28  33 
3427.85  19.50  27.77  19.62  27.68  19.74  |27.69j  19.86  34 
35  28.67  20.08)  28.58  20.20;  J28.49  20.32  ,28.41,20.451  35 
36i29.49  20.65  29.4020.78  ^29.31  20.91  29.22  21.03i  36 
37  30.31  21.22!  30.22  21.35  30. 12  21.49  30.03|21.62|  37 
3831.1321.80)31.0321.93  30.9422.07  30.84l22.20;  38 

3931.9522.37  31.85  22.51  !31.75j2i2.65  31.6522.79!  39| 
40.32.77  22.94  132.67  23.09jj32.56  23.23  32.46^.37  401 

41  31.5912^1  3^  23!66i|33.38|23.81  33.27  23.95i"4l| 

42  34.40i24.09  34.3024.24  J34.19l24.39  34.0924.54   42 1 
4335.2224.66  35.12  24.82  '35.01  i24.97  34.90125. 12i  431 
4436.0425.24  35.9325.39  !35.82j25.55  35.71:25.71   441 
4536.8625.81  36.7525.97  !36. 64:26.13  36.52  26.291  45| 

4637.6826.38  37.57  26.55  |37.45  26.71  j37.3326.88i  461 
47  38.50  26.96  38.38  27.13  38.26,27.29 J38. 14  27.46  47 1 
48>J9.32  27.53,  39.20  27.70J  39.08;27.87i|38.96|28.04 

49  40. 14!28. 1 1  40.02  28.28| |39.89  28.45  39.77  28.63 

50  40.96:28.68  40.83  28.86'  40.71  29.04!  40.5829.21 


DepJ  Lat.  ;Dep.   LatJ 


55 


TRAVERSE  TABLE. 


109 


5 

35  Deg. 

35jDeg. 

35ibeg.| 

35|Deg. 

0 

r 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

51 

1.78 

9.25 

1.65 

29.43 

1.52 

29.62 

41.39 

29.80 

51 

52 

2.60 

9.83 

42.47  30.01 

42.33 

30.20! 

42.20 

30.38 

52 

53 

43.42 

30.40 

43.28  30.59 

3.15 

30.78 

43.01 

30.97 

53 

54 
55 

44.23 
45.05 

30.97 
1.55 

44.1031.17 
4.9231.74 

3.96 
44.78 

31.36, 
31.94; 

43.8231.55 
44.64>32.13 

54 
55 

56 

5.87 

2.12 

5.7332.32 

45.59 

32.52 

45.4532.72 

56 

57 

6.69 

32.69 

46.55  32.90 

46.40 

33.10!  46.26  33.  30 

57 

58 

47.51 

33.27 

7.37  33.47 

47.22 

33.68!!47.0? 

33.89 

58 

59 

48.33 

33.84 

8.1834.05 

48.03 

34.26  47.88  34.47 

59 

60 

49.15 

34.41 

49.0034.63 

48.85 

34.84J  48.69  35.05 

60 

34.99 
35.56 

49.66 
50.48 

! 

49.5135.64 
50.32  36.22 

61 
62 

61 
62 

49.97 
50.79 

49.82!35.21 
50.6335.78 

35.42; 
36.00! 

63 

5L61 

36.14 

51.45!36.36 

61.29!36.58 

51.13 

36.81 

63 

64 

o2.43 

36.71 

52.2736.94 

52.1037.16!  51.94 

37.39   64 

65 

53.24 

37.28 

53.0837.51 

52.92  37.75  52.75 

37.98 

65 

66 

54.06 

37.86 

63.9038.09 

53.73'38.33  53.56 

38.56 

66 

67 

54.88 

38.43 

54.71|38.67 

54.5538.91  54.38 

39.14 

67 

68 

55.70 

39.00 

55,53  39.25 

55.36!39.49  55.19 

39.73 

68 

69 
70 

56.52 
57.34 

39.58 
40.15 

56.35 
57.16 

39.82 
40.40 

56.1740.07 

56.9940.65 

1          | 

56.00 
56.81 

40.31 
40.90 

69 
70 

71 

58.16 

40.72 

57.98 

40.98 

57.80l41.23  57.62 

41.48 

71 

72 

58.98 

41.30 

58.80 

41.55 

58.6241.81 

58.43 

42.07 

n 

59.80 

41.87 

59.61 

42.13 

59.43!42.39  69.24 

42.65 

73 

74 

60.62 

42.44 

60.43 

42.71 

60.24|42.97  !60.06 

43.23 

74 

75 

61.44 

43.02 

61.25 

43.29 

61.0643.55 

60.87 

43.82 

75 

76 

62.26 

43.59 

62.06 

43.86 

61.87|44.  13  !61.68  44.40 

76 

77 

63.07 

44.17 

62.88 

44.44 

62.69  44.71!  !62.49*1.99 

77 

78 

63.89 

44.74 

63.70 

45.02 

63.50  45.29!  ;63.30  45.57 

78 

79 

64.71 

45.31 

64.51 

45.59 

64.3245.88  64.1l|46.16 

79 

80 

65.53 

45.89 

65.33 

46.17 

65.13 

46.46 

64.9346.74  80 

8' 

66.35 

46.46 

66.15 

46.75 

65.94 

47.04 

65.74'47.32 

81 

82 
83 

67.17 
67.99 

47.03 
47.61 

66.9647.33 
67.7847.90 

66.7647.62  60.55;47.91 
67.6748.20,167.3648.49 

82 
83 

84 

68.81 

48.18 

68.6048.48 

68.39148.  78  168.  17149.08 

84 

85 

69.63 

48.75 

69.4149.06 

69.20 

49.38:68.9849.66   85 

86 

70.45 

49.33 

70.2349.63 

70.01 

49.94:69.8050.25;  86 

37 
88 

71.27 
72.09 

49.90 
50.47 

71.0550.21 
71.8650.79 

70.83  50.52 
71.64J51.10 

70.61  60.  8S;  87 
71.4251.41    88 

89 

72.90 

51.05 

72.68  51.37 

72.46'51.68 

72.2352.00;  89 

90 

73.72 

51.62 

73.50 

51.94 

73.27  52.26 

73.0452.58   90 

91 

74.54 

52.20 

74.31 

52.52 

74.08is2.84l  73.85 

53.17  91 

92 

75.36 

52.77 

75.13 

53.10 

74.90:53.42  74.66 

53.75  92 

9J 

76.18 

53.34 

75.95 

53.6 

75.71  54.01 

75.48 

54.34 

93 

77.00 

53.92 

76.76 

54.2 

76.5354.59 

76.29 

54.92!  94 

95 

77.82 

54.49 

77.58 

54.8 

77.3455.17 

S77.1C 

55.50  95 

96 

78.64 

55.06 

78.40 

55.4 

78.1655.75 

77.91 

56.09   % 

97 

79.46 

55.64 

79.21 

55.98 

78.97  56.33 

J78.72 

56.67 

97 

98 
99 

80.28 
81.10 

56.21 
56.78 

80.03 
80.85 

56.5 
57.14 

79.7856.91 
80.60  57.49 

79.53 
80.35 

57.26 

57.84 

98 

99 

100 

81.92 

57.36 

81.66 

57.7 

81.41 

58.07 

81.16  58,42  100 

4 

Dep 

Lat 

Dep. 

Lat 

Dep 

Lat. 

DepJ  Lat. 

^j 

.2 

i 

. 

.  -   -  - 

-  ^^ 

Q 

55  Deg 

54£Deg 

54i 

Deg. 

54iDeg.p 

Q 

110 


TRAVERSE  TABLE. 


H36  Deg. 

36iDeg. 

36£Deg. 

36  £  Deg. 

g 

e-f- 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

Lat. 

Dep.|  ft 

1 

0.81 

0.59 

0.81 

0.59 

0.80 

0.59 

0.80 

0.60 

1 

2 

,1.62 

1.18 

1.61 

1.18 

1.61 

1.19 

1.60 

1.20 

2 

3 

2.43 

1.76 

2.42 

1.77 

2.41 

1.78 

2.40 

1.79 

3 

4 

3.24 

2.35 

3.23 

2.37 

3.22 

2.38 

3.20 

2.39 

4 

5 

4.05 

2.94 

4.03 

2.96 

4.02 

2.97 

4.01 

2.99 

5 

6 

4.85 

3.53 

4.84 

3.56 

4.82 

3.57    4.81 

3.59 

6 

7 

5.66 

4.11 

5.65 

4.14 

5.63 

4.16 

5.61 

4.19 

7 

8 

6.47 

4.70 

6.45 

4.73 

6.43 

4.76 

6.41 

1.79 

6 

9 

7.28 

6.29 

7.26 

5.32 

7.23 

5.35    7.21 

5.38 

9 

10 

8.09 

5.88 

8.06 

5.91 

8.04 

5.95    8.01 

5.98 

10 

11 

8.90  6.47 

8.87 

6.50 

8.84 

6.54!    8.81 

6.58 

11 

12 

9.71 

7.05 

9.68 

7.10 

9.65 

7.14!    9.61 

7.18    12 

13  10.52 

7.64 

10.48 

7.69 

10.45 

7.73;  10.42 

7.78    13 

1411.33 

8.23 

11.29 

8.28 

11.25 

8.33  11.22 

8.38    14 

15'12.14 

8.82 

12.10 

8.87 

12.06 

8.92  12.02 

8.97 

15 

16  12.94 
17  13.75 

9.40|  12.90 
9.99I113.71 

9.46 
10.05 

12.86 
13.67 

9.52  12.82 
10.  Hi  13.62 

9.57    16 

io.nl  n 

1814.5610.58114.52 

10.64 

14.47 

10.71  14.42 

10.77J  18 

19  15.37 
2016.18 

11.17 
11.76 

15.32 
16.13 

11.23 
11.83 

15.27 
16.08 

11.30 
11.90 

15.22 
16.03 

11.37 
11.97 

19 
29 

21  16.99  12.34 
2217.8012.93 

16.94 
17.74 

12.42 
13.01 

16.88 
17.68 

12.49  16.83 
13.09  17.63 

12.56   21 
13.16   22 

2318.61  13.62 

18.55 

13.60 

18.49 

13.68  18.43 

13.76   23 

2419.4214.11 

19.35 

14.19 

19.29 

14.28i  19.23 

14.36   24 

25  20.23!  14.69 

20.16 

14.78 

20.10 

14.87  20.03 

14.96   25 

26  21.03  15.28  20.97 

15.37 

20.90 

15.47;  20.83 

15.56:  26 

27  21.84  15.87  ,21.77 

15.97 

21.70 

16.06  21.63 

16.15   27 

2822.65,16.46122.58 

16.56 

22.51 

16.65  22.44 

16.75  28 

29  23.46  17.05  J23.39 

17.15 

23.31 

17.25  23.24 

17.35   29 

3924.27 

17.63 

24.19 

17.74 

24.12 

17.84  24.04 

17.95  30 

31 

25.08  18.22 

25.00 

18.33 

24.92 

18.44  24.84 

18.55  31 

3225.89!18.81'|!25.81 

18.92 

25.72 

19.03;  25.64 

19.15   32 

33  26.  70|  19.  40  26.61 

19.51 

26.53 

19.63  26.44 

19.74'  S3 

3427.51  19.98  27.4220.10 
35!28.32  20.57  28.2320.70 
36  29.  12|21.16  29.0321.29 

27.33 
28.13 
28.94 

20.22 
20.82 
21.41 

27.24 
28.04 
28.85 

20.34 
20.94 
21.54 

34 
35 

37  29.93J21.75 

29.84 

21.88 

29.74 

22.01 

29.65 

22.14 

37 

38 

30.7422.34 

30.64 

22.47 

30.55 

22.60 

30.45 

22.74 

38 

3931.55J22.92 

31.45 

23.06 

31.35 

23.20 

31.25 

23.33 

39 

4032.3623.51 

32.26 

23.65 

32.15 

23.79 

32.05 

23.93 

40 


4133.1724.10 
4233.9824.69 
4334.7925.27 
44'35.6025.86 

33.06 
33.87 
34.68 
35.48 

24.24 
24.83 
25.43 
26.02 

32.96 
33.76 

34.57 
35.37 

24.39 
24.98 
25.58 
26.17 

32.85 
33.65 
34.45 
35.26 

24.53 
25.13 
25.73 
26.83 

41 

42 
43 
44 

45136.41  26.45 

36.29 

26.61 

36.17 

26.77 

36.06 

26.92 

45 

46  37.21  27.64 

37.10 

27.20 

36.98 

27.36 

36.86 

27.52   46 

47  38.02  27.63  ;37.90 

27.79 

37.78 

27.96!  37.66 

28.12|  47 

48'38.83  28.2l|  138.71 
49  39.64  28,80  39.52 

28.38 
28.97 

38.59 
39.39 

28.55 
29.15 

38.46 
39.26 

28.72   48 
29.32  49 

50 

40.45 

29.39 

40.32 

29.57 

40.19 

29.74 

^0.06 

29.92 

50 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

-£ 

s 

54  Deg. 

53  J  Deg. 

oSJDeg. 

53  J  Deg. 

5 

TRAVERSE  TABLE. 


y36  Deg.| 

36iDeg.  36iDeg, 

36,Deg. 

o 

?*•   Lat.;  Dep. 
514K2629.98! 

Lat.  Dep. 
41.1330.16 

Lat. 
!41.00 

Dep. 

30.34; 

Lat. 

40.86 

Dep. 
30.51 

p.* 

51 

5242.0730.56 

41.9430.75 

41.8030.93; 

41.6731.11 

52; 

5342.8831.15 

42.74,31.34 

42.60131.53 

42.4731.71 

53 

54143.  69  31.  74 

43.5531.93 

43.41 

32.12 

43.27  32.31 

54 

5544.5032.33 

44.35:32.52 

44.21 

32.72; 

44.07  32.91 

55 

5645.3032.92 

45.1633.11 

45.02 

33.31 

44.87 

33.51 

56 

5746.1133.50 

45.97'33.70 

45.82 

33.90 

45.6734.10 

57 

58  46.92 

34.09 

46.7734.30 

46.62l34.50: 

46.47  34.70 

58 

5947.73 

34.68'  47.58  34.89 

47.4335.09 

47.2735.30 

59 

6048.54 

35.27|  48.39i35.48 

48.2335.69 

48.0835.90 

60 

_____ 

_____ 

1  

61  49.35 
6250.16 

35.85 
36.44 

49.1936.07 
50.00  36.66 

49.0436.28 
49.8436.88 

48.8836.50 
49.6837.10 

61 

62 

63  50.97  37.03 

50.8137.25*50.64137.47 

50.48 

37.69!  63 

64;51.  78  37.62 

51.61J37.84 

51.4538.07 

51.28 

38.29   64 

65152.59  38.21 

52.42J38.44 

52.2538.66 

52.08 

38.89   65 

38.79 

53.23I39.03 

53.05  39.26 

52.88 

39.49J  66 

€754.2039.38 

54.0339.62 

53.86 

39.85 

53.68 

40.09J  67 

68;55.01  39.97 

54.84J40.21 

54.66 

40.45 

54,49 

40.69|  68 

69|55.82  40.56 

55,64  40.80 

55.47 

41.04 

55.29 

41.28 

69 

7056.6341.14 

56.4541.39 

56.27 

41.64 

66.09 

41.88 

70 

7157.4441.73 

57.26 

41.98 

57.07 

42.23 

56.89 

42.48 

71 

72  58.25  42.32 

58.06  42.57 

57.88 

42.83 

57.69 

43.08 

72 

73:69.0642.91 

58.8743.17 

58.68 

43.42 

58.49 

43.68 

73 

74;59.87!43.50 

59.68'43.76 

59.49  44,02 

59.29 

44.28 

74 

7560.6844.08 

60.48  44.35 

60.29  44.61 

60.09 

44.87 

75 

7661.49:44.67 

61.2944.94 

61.09i45.21 

60.90  45.47 

76 

77  62.29  45.26 

62.1045.53 

61.9045.80 

61.7046.07 

77 

7863.1045.85 

62.9046.12 

62.7046.40 

62.50 

46.67 

78 

7963.9146.43 

63.71 

46.71 

63.5046.99 

63.30 

47.27 

79 

8064.7247.02 

64.52 

47.30 

64.31  47.69 

64.10 

47.87 

80 

81J65.53!47.61 

65.3247.90 

65.11 

48.18 

64.90 

48.46   81 

82:66.34  48.20 

66.13J48.49 

65.92 

48.78 

65.70 

49.06i  82 

8367.15 

48.79 

66.93 

49.08 

66.72 

49.37 

66.50 

49.66!  83 

84|67.96  49.37 

67.7449.67 

67.52 

49.97 

67.31 

50.26   84 

85  68.77  49,96 

68.55  50.26 

68.33 

50.56 

68.11 

50.861  85 

86  69.58  50.55 

69.3550.85 

69.13 

51.15 

68.91 

51.46!  86 

8770.38:51.14 

70.1651.44 

69.94 

51.75 

69.71 

52.05,  87 

8871.19151.73 

70.9752.04 

70.74 

52.34  170.51 

52.65   88 

89  72.00!52.31 

71.7752.63 

71.54 

52.94 

71.31 

53.25i  89 

90  72.81  52.90 

72.5853.22 

72.35 

53.53 

72.11 

53.85   90 

i 

91  73.62 

53.49 

73.39  53.81 

'73.15 

54.13 

72.91 

54.45   91 

92  74.43  54.08 

74.1954.40 

73.95 

54.72 

73.7255.05   92 

93j75.24;54.66 

75.00:54.99 

74.76  55.32 

74.5255.64   93 

9476.0555.25 

75.8155.58 

75.56  55.91 

75.3256.24;  94 

95,76.8655.84 

76.61j56.17 

76.37  56.51 

76.  12156.84;  95 

96  77.67  56.43 
97|78.47;57.02 

77.42.56.77 
78.23:57.36 

77.17 
77.97 

57.10  76.9257.44   96 
57.70  77.7258.04   97 

98179.2857.60 

79.03|57.95 

78.78 

58.29 

78.52 

58.64   98 

99  i  80.09  58.  19; 

79.84i58.54 

79.58 

58.89 

79.32 

59.23   §9 

100  80.90 

58.781 

80.6459.13  80.39 

59.48 

80.13 

59.83  100 

*J  Dep. 

.2 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.  -55 

Q  54  Deg.! 

53£Deg. 

53peg.i 

53|Deg.Q 

212 


TRAVERSE  TABLE. 


g 

37  Deg 

37£Deg 

37~£Deg 

37'Deg 

o 

3? 

«-( 

Lat 

Dep 

Lat. 

Dep 

Lat 

Dep 

Lat 

Dep 

c 

0.8 

0.6 

0.80 

0,6 

0.79 

0.6 

0.7S 

0.6 

1.6 

1.2 

1.59 

1.2 

1.59 

1.2 

1.56 

1.2$ 

! 

2.4 

1.8 

2.39 

1.85 

2.38 

1.8 

2.37 

l.fr 

3.1 

2.4 

3.18 

2.4$ 

3.17 

2.43 

3.16 

2.4< 

3.9< 

3.0 

3.98 

3.0i 

3.97 

3.04 

3.95 

3.0* 

l 

4.7J 

3.6 

4.78 

3.6£ 

4.76 

3.65 

4.74 

3.6' 

5.5S 

4.2 

5.57 

4.24 

5.55 

4.2 

5.53 

4.2J 

J 

6.3S 

4.8 

6.37 

4.84 

6.35 

4.8 

6.33 

4.9C 

c 

7.18 

5.42 

7.16 

5.45 

7.14 

5.4 

7.12 

5.51 

1C 

7.99 

6.02 

7.96 

6.05 

7.93 

6.09 

7.91 

6.12 

1 

11 

8.78 

6.62 

8.76, 

6.66 

8.73 

6.70 

8.70 

6.73 

12 

9.58 

7.22 

9.55 

7.26 

9.52 

7.31 

9.49 

7.35 

13 

10.38 

7.82 

10.35| 

7.87 

10.31 

7.91 

10.28 

7.96 

14 

11.18 

8.43 

11.14 

8.47 

11.11 

8.52 

11.07 

8.57 

25 

11.98 

9.03 

11.94 

9.08 

11.901 

9.13 

11.86 

9.18 

16 

12.78 

9.63 

12.74 

9.68 

12.691 

9.74 

12.65 

9.80 

17 

13.58 

10.23 

13.5310.29 

13.4910.36 

13.4410.41 

18 

14.38 

10.83 

14.3310.90 

4,2810.9 

14.2311.02 

19 

16.17 

11.43 

15.12jll.50 

15.07111.57 

15.0211.63 

20 

15.97 

12.04 

15.92 

12.11 

15.87 

12.18 

15.81 

12.24 

2 

21 

16.77 

12.64 

16.72  12.71 

16.66  12.78 

16.60  12.86 

21 

22 

17.57 

3.24 

17.51!  13.32 

17.451  13.39 

7.40  13.47 

22 

23 

18.37 

3.84 

18.3113.92 

18.2514.00 

«.  1914*08 

23 

24 

19.17 

4.44 

19,1014.53 

119.0414.61 

8.98  W.69 

24 

25 

19.97 

5.05 

19.9015.13 

M.83J15.22 

9.77  15.31 

25 

26 

20.76 

5.65 

20.7016.74 

20.63!  15.83 

0.5615.92 

26 

27 

1.56 

6.25 

21.4916.34 

21.42  16.44 

1.3516.53 

27 

28 

522.36 

16.85 

22,2916.95 

22.21  17,05 

2.1417.14  28 

29 

23.16 

17.45 

23.08  17,55 

23.0117.65 

2.9317.75  29 

30 

23.96 

18.05 

23.8818.16 

23.80118.26 

23.72  18.37 

SO 

i 

1  

31 

24.76 

18.66 

24.6818.76 

24.59  1 

8.87 

24.51  18.98 

31 

32 

25.56 

19.26 

25.4719.37 

26.39  1 

9.48 

5.3019.59 

32 

33 

26.35 

19.86 

26.27  19.97 

26.1820.09! 

6.0920.20 

33 

34 

27.15 

20.46 

27.0620.58  26.9720.70 

6.8820.82 

34 

35 

27.95 

21.06 

27.8621.19  27.7721.31 

7.6721.43 

35 

36 

28.75 

21.67 

28.6621.79 

28.5621.92 

8.46  22.04 

36 

37 

29.55 

22.27 

29.4522.40 

29.3522.52 

9.2622.65 

37 

38 

30.35 

22.87 

30.25  23.00 

30.1523.13 

30.0523.26 

38 

39 

$1.15 

23.47 

31.0423.61 

30.94'23.74 

30.8423.88 

39 

40 

31.95 

24.0 

31.8424.21 

i  . 

31.7324.35 

1.6324.49 

40 

41 

42 

32.74 
33.54 

24.67 
>5.28 

32.6424.82 
33.4325.42 

32.53;24.96 
33.3226.57 

2.4225.10 
33.2125.71 

41 
42 

43 

34.34 

25.88 

34.23  26.03 

34.1126.18 

34.0026.33 

43 

44 

35.14 

26.48 

35.02  26.63 

34.91,26.79 

34.  79;  26.94 

44 

45 

J5.94 

J7.08 

35.8227.24 

35.7027.39 

5.58|27.55 

45 

46 

36.74 

J7.68 

36.6227.84 

36.4928.00 

36.3728.16 

46 

47 

37.54 

>8.29 

37.4128.46 

37.29'28.61 

7.1628.77 

47 

48 

18.33 

18,89 

38.21  29.05 

38.08  29.22 

7.95J29.39 

48 

49 

$9.13 

59.49 

39.0029.66 

38.8729.83 

8.74  30.00 

49 

50 

(9.93 

50.09 

39.803- 

0.26 

39.67J  30.44 

9.53  30.61 

50 

3 

CtepT 

Lat 

DepJ  Lat. 

Dep.  Lat. 

ep. 

Lat. 

S 

P 

53  Deg. 

62?Deg. 

52iDeg. 

2iDeg. 

1*4 

TRAVERSE  TABLE. 


113 


g 

37  Deg. 

37±Deg. 

371  Deg. 

37|Deg. 

e 

r 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

51 

40.73 

30.  £9 

40.60 

30.87 

40.46 

31.05 

40.33 

31.22 

51 

52 

41.53 

31.29 

41.39 

31.48 

41.26 

31.66 

41.12 

31.84 

52 

53 

42.33 

31.90 

42.19 

32.08 

42.05 

32.26 

41.91 

32.45 

53 

5443.13 

32.50 

42.96 

32.69 

42.84 

32.87 

42.70 

33.06 

54 

55 

43.92 

33.10 

43.78 

33.29 

43.63 

33.48 

43.49 

33.67 

55 

56 

44.72 

33.70 

44.58 

33.90 

44.43 

34.09 

44.28 

34.28 

56 

57  45.52 

34.30 

45.37 

34.50 

45.22 

34.70 

45.07 

34.90 

57 

58  46.32 
5947.12 

34.91 
35.51 

46.17 
46.96 

35.11 
35.71 

46.01 
46.81 

35.31 
35.92 

45.86 
46.65 

35.51 
36.12 

58 
59 

6047.92 

36.11 

47.76 

36.32 

47.60 

36.53 

47.44 

36.73 

60 

I  

6148.72 

36.71 

48.56 

36.92 

48.39 

37.13 

48.23 

37.35 

61 

62,49.52 

37.31 

49.35 

37.53 

49.19 

37.74 

49.02 

37.96 

62 

6350.31 

37.91 

50.15 

38.13 

49.98 

38.35 

49.81 

38.57 

63 

6451.11 

38.52 

50.94 

38.74 

50.77i88.96 

50.60 

39.18 

64 

6551.91 

39.12 

51.74 

39.34 

51.57  39.57 

51.89 

39.79 

65 

6652.71 

39.72 

52.54 

39.96 

52.36i40.18 

52.19 

40.41 

66 

6763.51 

40.32 

53.33 

40.55 

53.15140.79 

52.98 

41.02 

67 

68  54.31 

40.92 

54.13 

41.16 

53.95141.40 

53.77 

41.63 

68 

69 

55.11 

41.53 

54.92 

41.77 

54.74 

42.00 

54.56 

42.24 

69 

70 

55.90 

42.13 

65.72 

42.37 

55.53 

42.61 

55.35 

42.86 

70 

71 

56.70 

42.73 

56.52 

42.98 

66.33 

43.22 

56.14 

43.47 

71 

72 

57.50 

43.33 

57.31 

43.58 

57.12 

43.83 

56.93 

44.08 

72 

73 

58.30 

43.93 

58.11 

44.19 

67.91  44.44 

57.72 

44.69 

73 

74 

59.10 

44.63 

58.90 

44.79 

58.71  45.05 

58.51 

45.30 

74 

75 

59.90 

45.14 

59.70 

46.40 

59.5045.66 

59.30 

45.92 

75 

76 

60.70 

45.74 

60.50 

46.00 

60.29  46.27 

60.09 

46.53 

76 

77 

61.49 

46.34 

61.29 

46.61 

61.09:46.87 

60.88 

47.14 

77 

78 

62.29 

46.94 

62.09 

47.21 

61.88:47.48 

61.67 

47.75 

78 

79 

63.09 

47.54 

62.88 

47.82 

62.67,49.09 

62.46 

48.37 

79 

80 

63.89 

48.15 

63.68 

48.42 

63.47 

48.70 

63.26 

48.98 

80 

81 

64.69 

48.75 

64.48 

49.03 

64.26 

49.31 

64.05 

49.59 

81 

82 

65.49 

49.35 

65.27 

49.63 

66.05  49.92 

64.84 

60.20 

82 

83 

66.29 

49.95 

66.07 

50.24 

65.86  50.53 

65.63 

50.81 

83 

84 

67.09 

50.55 

66.86 

50.84 

66.64 

51.14 

66.42 

61.43 

84 

85 

67.88 

51.15 

67.66 

51.45 

67.43 

51.74 

67.21 

52.04 

85 

86 

68.68 

51.76 

68.46 

52.06 

68.23 

52.35 

68.00 

52.65 

86 

87 

69.48 

52.36 

69.25 

52.66 

69.02 

52.96 

68.79 

53.26 

87 

88 

70.28 

52.96 

70.05 

53.27 

69.82 

53.57 

69.58 

53.88 

88 

89 

71.08 

53.56 

70.84 

53.87 

70.61 

64.18 

70.37 

54.49 

89 

90 

71.8S 

54.16 

71.64 

54.48 

71.40 

54.79 

71.16 

55.10 

90 

91 

72.68 

54.77 

72.44 

65.08 

72.20 

55.40 

71.95 

56.71 

91 

92 

73.47 

55.37 

73.23 

55.69 

72.99J56.01 

72.74 

56.32 

92 

93 

74.27 

55.97 

74.03 

56.29 

73.7866.61 

73.53 

56.94 

93 

94 

75.07 

56.57 

74.82 

56.90 

74.68:57.22 

74.32 

57.55 

94 

95 
96 

75.87 
76.67 

57.17 
57.77 

75.62 
76.42 

57.50 
58.11 

75.37J57.83 
76.1658.44 

75.12 
75.91 

58.16 
58.77 

95 

86 

97 

77.47 

58.38 

77.21 

58.71 

76.96!59.05 

76.70 

59.39 

97 

98 

78.27 

58.98 

78.01 

59.32 

77.75  59.66 

77.49 

60.00 

98 

99 

79.06 

59.58 

78.80 

59.92 

78.64)60.27 

78.28 

60.61 

99 

100 

79.86 

60.18 

79.60 

60.53 

79.34(60.88 

79.07 

61.22 

100 

« 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

« 

s 

53  Deg. 

52|Deg. 

52£Deg. 

o2tDeg. 

a, 

114 


TRAVERSE  TABLE. 


g 

38  Deg. 

38fDeg. 

38  J  Dec. 

38£Deg. 

O 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

O> 

j 

0.79 

0.62 

0.79 

0.621 

0.78 

0.62 

0.78 

0.63 

1 

2 

1.58 

1.23 

1.67 

1.24  i 

1.67 

1.24 

1.56 

1.26 

2 

3 

2.36 

1.85 

2.36 

1.86| 

2.35 

1.87 

2.34 

1.88 

3 

4 

3.15 

2.46 

3.14 

2.48  1 

3.13 

2.49 

3.12 

2.5C 

4 

5 

3.94 

3.08 

3.93 

3.  1C1 

3.91 

3.11 

3.90 

3.13 

5 

6 

4.73 

3.69 

4.71 

3.71  ! 

4.70 

3.74 

4.68 

3.76 

6 

7 

5.52 

4.31 

5.50 

4.33  j 

5.48 

4.36 

5.46 

4.38 

7 

8 

6.30 

4.93 

6.28 

4.95! 

6.26 

4.98 

6.24 

5.01 

8 

9 

7.09 

5.54 

7.07 

5.571 

7.04 

6.60 

7.02 

5.63 

9 

10 

7.88 

6.16 

7.85 

6.19 

7.83 

6.23 

7.80 

6.26 

10 

11 

8.67 

6.77 

8.64 

6.81 

8.61 

6.85 

8.58 

6.89 

11 

12 

9.46 

7.39 

9.42 

7.431 

9.39 

7.47 

9.'36 

7.51 

12 

13 

10.24 

8.00 

10.21 

8.05 

10.17 

8.09 

10.14 

8.K 

IS 

14 

11.03 

8.62 

10.99 

8.67 

10.96 

8.72 

10.92 

8.76 

14 

15 

11,82 

9.23 

11.78 

9.29 

11.74 

9.34 

11.70 

9.39 

15 

16 

12.61 

9.85 

19.57 

9.91 

12.52 

9.96 

12.48 

10.0] 

16 

17 

13.40 

10.47 

13.35 

10.52 

13.30 

10.58 

13.26 

10.64 

17 

18 

14.18 

ll.Oi 

14.14 

11.14 

14.09 

11.21 

P1.04 

11.21 

IS 

19 

14.97 

11.70 

14.92 

11.76 

14.87 

11.B3 

14.82 

11.89 

19 

20 

15.76 

12.31 

15.71 

12.38 

15.65 

12.45 

15.60 

12.52 

20 

21 

16.55 

12.93 

16.49 

13.00 

16.43 

13.07 

16.38 

13.14 

21 

22 

17.34 

13.54 

17.28 

13.62 

17.22 

13.70 

17.16 

13.77 

22 

23 

18.12 

14.16 

18.06 

14.24 

18.00 

14.32 

17.94 

14.4( 

2S 

24 

18.91 

14.78 

is.a^ 

14.86 

18.78 

14.94 

18.72 

15.02 

24 

25 

19.70 

15.39 

19.63 

15.48 

19.57 

15.56 

19.50 

15.65 

25 

26 

20.4J 

16.01 

20.42 

16.10 

20.& 

16.19 

2G.28 

16.2' 

26 

27 

21.28 

16.62 

21.20 

16.72 

21.  IS 

16.81 

21.06 

16.90 

27 

28 

22.06 

17.24 

21.99 

17.33 

21.91 

17.43 

21.84 

17.53 

28 

29 

22.85 

17.85 

22.7- 

17.95 

22.7C 

18.05 

22.62 

18.15 

29 

30 

23.64 

18.47 

23.56 

18.67 

23.48 

18.68 

23.40 

18.78 

30 

31 

24.4.S 

19.09 

24.34 

19.19 

24.26 

19.30 

24.18 

19.40 

31 

32 

25.22 

19.70 

25.  If 

19.81 

26.04 

19.92 

24.96 

20.03 

32 

33  26.00 

20.32 

25.92 

20.43 

2^.8L 

20.54 

25.74 

20.66 

33 

34 

26.  7S 

20.93 

26.  7f 

21.05 

26.6J 

21.17 

26.52 

21.28 

34 

35 

27.58 

21.55 

27.49 

21.67 

27.39 

21.79 

27.30 

21.9 

35 

36 

28.87 

29,,  16 

28.9,7 

22.29 

28.1- 

22.41 

28.08 

22.53 

36 

37|29.16 

22.78 

29.06 

22.91 

28.96 

23.03 

28.86 

23.16 

37 

38 

29.94 

23.40 

29.84 

23.53 

29.74 

23.66 

29.64 

23.79 

38 

39 

30.73 

24.01  190.63 

24.14 

30.62 

24.28 

30.42 

24.41 

39 

40 

31.52 

24.63  |S1.41 

i 

24.76 

31.  30 

24.90 

31.20 

25.04 

40 

41 

32.31 

25.24  I32.2C 

26.38 

32,0! 

-.5.52 

31.98 

25.66 

41 

42 

33.10 

25.86 

182.98 

26.00 

32.8" 

26.15 

32.76 

26.29 

42 

4333.88 

26.47 

[83.77 

26.62 

33.66 

26.7- 

33.5S 

26.91 

43 

4434.67 

27.09 

'34.  5£ 

27.24 

34.4S 

27.39 

34.31 

27.54 

4 

45'35.46 

27.70 

'35.34 

27.86 

35.22 

28.0 

35.09 

28.17 

45 

46136.25 
47  37.04 

28.32 
28.94 

36.12 
'36.9 

28.48 
29.10 

36.0C 
36.78 

28.64 
29.26 

36.87128.79 
36.65J29.42 

46 

47 

48.37.82 

29.55 

37.70 

29.72 

37.5- 

29.88 

37.43130.04 

48 

49138.6 

30.17 

38.48 

30.34 

38.35 

30.50 

38.2130.67 

49 

SO 

39.40 

30.78 

39.27 

30.96 

39.13 

31.13 

38.9931.30 

60 

t| 

Dep 

Lat. 

Dep 

Lat. 

Dep 

Lat 

Dep.j  Lat. 

.+J 

CO 

3 

52  Deji. 

>51fDeg. 

51£Deg 

51iDeg. 

2 

TRAVERSE  TABLE. 


•   115 


56  44. 13  34.48|  143.98 
7  44.92  35.09 


59 


5.7035.71 
6.49  36.32| 
7.28  36.94 

8.07  37.£ 
8.8638.1: 
9.64  38.79] 
0.43  39.40| 
..22  40.1 
2.0140. 
2.8041.25] 


IOC 


8  Deg, 
Lat.  Dep. 


U931. 
0.9832.011 


.7632.63  41.62 

.5533.25  42.41 


3.34 


Lat. 

).05 
140.84 


33.86  43.19 


>4.37|42.4 


76 
45.55 
46.33 
47.12 

|47.90 
69 
.47 
26 

51.05 

51.83 
62 
40 

54.19 


5. 16 j43. 10  1 54.97 


5.95I43.711 
56.74]44.: 
7.52:41.94] 

8.3145.56 
9.10,46.17! 
.9.8946.' 
60.68:47.41 
11.4648.1 
12.25:48.64] 


55.76 


CJK 

.57 
2.19 
J.81 
J.43 
J4.05 
4.67 
.29 
.91 
S.53 
7.15 


7.76 
8.38 
9.00 
9.62 
0.24 
0.86 
1.48 
2.10 
2  72 
3'.34 


3.96 


56.5444.57 


57.33 


5.19 


63.04  49.25  62.83  49.53 


53.83  49.87 
54.6260.48 
J5.4051.10 


63.6 
64.4 
65.1 


56.1951.72  65.9 

56.98  52.33  66,7 

7.7752.95  67,5 

58.5653.56  68.3 


69.3454.1 
70.13  54. 


69.1 
69.8 


9070.9255.41  70.6 


71.7156.03 
9    72.5056.64 

93  73.28  57.! 
9    74.0757.87] 

74.8658.4! 

75.6559.10] 

76.44  59.7i 
9    77.2260.! 

78.0160.95] 


71.4 

72.2 
73.0 
73.8 
74.6 

5.3 
76.1 
176.9 

77.7 


78.8061.57  78.5 


Dep.  |  Lat.  Dep    La 


9.91 
).70 

.48 


44.61 

5.39 

.17 

6.96 


58. 

58.9( 

59.6 

60.4 

61.2. 

62.04  48.9 


5.81 
6.43 

:7.05 

:7.67 


>0.7 

>i.3£ 

i2.0( 
>2.6C 
iS.2 
.3.8 
i4.4 
55.1 
55.7 

56.3 
56.9 
57.5 
58.1 
58.8 
59.4 
60.0 
60.6 
61.2 
61.9 


Q  52  Deg.ll51fDeg 


2.37  40.55132.55 
fc.99  41.33  S3.  J7 
3.62142. 11 133.80 
$4.24442.8934.43 
4.86J  143.67  35.05 
5.48  44.45  35.68 
6.11  45.23'36.30 
6.73!!46.01J36.93 
7.35!  48.79  37.56 


7.74  37.97 


8.52 
9.30 
0.09 
).87l 
1.65 


4.00 

4.78 


8.60 

9.221 


5.5' 

6.35 

7.13 

7.9 

8.7( 

9.4f 

0.2f 

1.04 

l.8£ 

2.6 

63.3 

49 
65.7 

6.5 
57.3 
58.0 
58.8 
59.6 
70.4 


71.2 
2.0 
72.7 
73.5 
74.3 
75.1 
75.9 
76.7 
77. 
78.2 


47.57  38.18 
48.35  38.81 
49. 13  !39.43 

9.84J  49.91  [40.06 

0.46 

1.09 

1.71 


2.33 
42.95 

3.58 


44.82 

45.44 
6.07 

46.69 
J.31 
7.93 
S8.56 
[9.18 

49.80 


>0.42 
51.05 
il.67 


s^ueg.  „ 


50.69  40.68 
51.47  41.31 
52.25  41.9 
53.03  42.56 
53.81  43.19 
54.59  43.8 


4.20  55.3744.44 
56.15  45.07 
56.93  45.6i 
57.7146.32 
58.4946.94 
59.2747.5' 
60.05  48.2C 
60.83  48.8! 
61.6149.4 
62.39150.0 


63. 17  50. 7' 
63.9551.3 
164.7351.9 
52.291 '65.51 152.5 
52.91 1 166.29  ;53.2 
53.54!  |67.07'53.8 
54.16]i67.85'54.4 
54.78:168.63:55.0 
55.40  69.41  55.7 
56.03  70.19  56.3 


56.65  70.97  56.9 
57.2?!  71.75  57.5 
57.89J  72.53  68.2 
58.52-73.3158.8 
59.14  74.0959.4 
59.76fi74.87  60.0 
60.38!  75.65  60.7 
81.01]  76.43  61.! 
61.63  77.21  61.9 
62.25]  77.99  62.5  100 


Dep    Lat. 


Dep.   Lat 


116 


TRAVERSE  TABLE. 


s 

39  Deg. 

39£Deg. 

39£Deg. 

39|Deg. 

o 

cr> 

r^ 

Lat. 

pep. 

Lat.  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

£ 

1 

0.78 

0.63 

0.77J  0.63 

0.77 

0.64 

0.77 

0.64 

] 

2 

1.55 

1.26 

1.55    1.27 

1.54 

1.27 

1.54 

1.28 

2 

3 

2.33 

1.89 

2.32   1.90 

2.31 

1.91 

2.31 

1.92 

3 

4 

3.11 

2.52 

3.10  2.53J 

3.09 

2.54 

3.08 

2.56 

4 

5 

3.89 

3.15 

3.87 

3.161 

3.86 

3.18 

3.84 

3.20 

5 

6 

4.66 

3.78 

4.65 

3.80 

4.63 

3.82 

4.61 

3.84 

6 

7 

5.44 

4.41 

5.42 

4.43 

5.40 

4.45 

5.38 

4.48 

7 

8 

6.22 

5.03 

6.20 

5.06 

6.17 

5.09 

6.15 

5.12 

8 

9 

6.99 

5.66 

6.97 

5.69 

6.94 

5.72 

6.92 

5.75 

9 

10 

7.77 

6.29 

7.74  6.33 

7.72 

6.36 

7.69 

6.39 

10 

11 

8.55 

6.92 

8.52   6.96 

8.49 

7.00 

8.43 

7.03 

11 

12 

9.33 

7.55 

9.29    7.59 

9.26 

7.63 

9.23 

7.67 

12 

13 

10.10 

8.  IS 

[0.07    8.23 

10.03 

fi.27 

9,99 

8.31 

13 

14 

10.88 

8.81 

10.84   8.86 

10.80 

8.91 

10.76 

8.95 

14 

15 

11.66 

9.44 

11.62   9.49 

11.57 

9.54 

11.53 

9.59 

15 

16  12.43  10.07 

12.3910.12 

12.35 

10.18 

12.30 

10.23 

16 

17  13.21 

10.70 

[3.1610.76: 

13.12  10.81 

13.07 

10.87 

17 

18  13.99  ll.a<J 

13.9411.39 

13.89111.45 

13.84 

11.51 

18 

19 

20 

1477  11.96 
15.5412.59 

14.71 

15.49 

16.26 

12.02 
12.65 

14.66 
15.43 

12.09 
12.72 

13.36 

14.61 
15.38 

16.15 

12.15 
12.79 

13^43 

19 
20 

2l|l6.32  13.22 

13.29 

16.20 

21 

22  17.10  13.84 

[7.04J13.92 

16.98 

13.99 

16.91 

14.07   22 

2317.87114.47 
241  18.  65  15.  10 

17.81 
18.59 

14.55 
15.18 

17.75 

18.52 

14.63 
15.27 

17.68 
18.45 

14.71    23 
15.35   24 

25!  19.43  15.  73! 

19.36 

15.82 

19.9.9 

15.90 

19.22 

15.99   25 

2820&1 

16.36 

20.13 

16.45!  J20.06  16.54 

19.9916.63   26 

27i20.98  16.99 

20.91 

17.08 

20.83 

17.17 

20.76  17.26 

27 

28'21.76  17.62 

21.68 

17.72 

21.61 

17.81 

21.53117.90 

28 

29!22.54'  18.25! 

22.46 

18.35! 

22.38 

18.45 

22.3018.541 

29 

30,23.31 

18.88 

23.23 

18.98 

23.15 

19.08 

23.07 

19.18 

30 

31J24.09  19.51 

24.01 

19.61 

23.92 

19.72 

23.8319.82 

31 

3224.87:20.14 
3325.6520.77 
34  26.42l21.40 
3527.2022.03 
3627.9822.66 
37  28.75  23.28 
38  29.53  23.91 

24.78  20.251 
25.5520.88! 
26.3321.51 
27.1022.14 
27.8822.78 
28.6523.41 
29.4324.04 

24.69 
25.46 
26.24 
27.01 
27.78 
28.55 
29.32 

20.35 
20.99 
21.63 
22.26 
22.90 
23.53 
24.17 

24.6020.46 
25.3721.10 
26.14J21.74 
26.91J22.38 
27.68'23.02 
28.45123.66 
29.2224.30 

32 
33 
34 
85 
36 
37 
38 

39  30.31  '24.54 
4031.0925.17 

30.20  24.68  |30.09 
30.98J25.31  130.86 

24.81 
25.44 

29.9824.94 

130.75  25.58 

39 

41 

31.86i25.80 

31.75  25.^94 

31.64 

26.08 

31.5226.22  41 

42  32.64'26.43 

32.5226.57 

32.41 

26.72 

3£.29:2S.86  42 

43J33.42  27.06 

33.3027.21 

33.18 

27.35 

33,0627.50  43 

4434.19 

27.69 

(4.07  27.84 

33.95 

27.99 

33.83'28.14   44 

45'34.97 

28.32 

34.85 

28.47 

34.72 

28.62 

34.  60)28.77 

45 

46!35.  75  28.95 

35.62 

29.10 

35.49 

29.26 

35.3729.41    46 

47  36.53  29.58 

36.40 

29.74 

36.27 

29.90 

36.1430.05   47 

4837.3030.21 
49!38.08  30.84 
50'S8.86  31.47 

37.17 
37.95 

38.72 

30.37 
31.00 
31.64 

37.04 
37.81 

38.58 

30.53 
31.17 
31.80 

36.90 
37.67 
38.44 

30.69   48 
31.33  49 
31.97J  50 

« 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

L*t.  £ 

a 

51  Peg. 

SOfDeg. 

50iDegJ 

501  Deg.  6; 

TRAVERSE  TABLE. 


Deg. 

••JO  ^ 

Deg. 

39^  Deg. 

392  Deg. 

g 

r* 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.  |  Dep. 

r~ 

51 

39.6332.10 

39.4932.27:39.35 

32.44 

39.2132.61 

51 

52'40.41 

32.72 

40.27iS2.90  '40.  12 

33.08 

39.9833.25 

52 

5341.1933.35 

41.0433.53:40.9033.71 

140.7533.89 

53 

54:41.97133.98 

41.82  34.17  41.67  34.35  41.52,34.53 

54 

5542.74|34.61 
5643.52|35.24 

42.59  34.80  42.44  34.98  42.29  35.17 
43.37  35.43  43.21  35.621  43.06'35.81 

55 
56 

5744.3035.87 

44.14i36.06  43.98  36.26  43.8236.45 

57 

08  45.07  36.50 

44.91  36.70  44.75  36.89J  44.59  37.09 

58 

5945.8537.13! 

45.69  37.33  45.53;37.53i  45.3637.73 

59 

6046.63^7.76! 

46.46:37.96  46.3038.16 

46.1338.37 

60 

61 

47.41  38.39  47.2438.60  47.07  38.80 

46.90 

39.01 

61 

62 

48.1839.02 

48.01  39.23  147.8439.44 

47,67 

39.65 

62 

63148.96  39.65! 

48.7939.86  48.61 

40.07 

48.44 

40.28 

63 

64k9.74  40.28,  49.56<40.49  ;49.38  40.71 

49.21 

40.92 

64 

65150.51  40.91 

50.3441.13  50.1641.35 

49.97 

41.56 

65 

6651.2941.64 

51.1141.76  50.9341.98 

50.74 

42.20 

66 

6752.0742.16: 

51.8842.39/51.7042.62 

51.51 

42.84 

67 

6852.8542.79! 

52.66l43.02i  52.47  43.25 

52.28 

43.48 

68 

6953.5243.42 

53.4343.66  53.2443.89 

53.05 

44.12 

69 

7054.4044.05 

54.21  44.29  54.01  44.53 

53.82 

44.76 

70 

71!55.1844.68 

54.9844.92  54.7945.16 

54.59 

45.40 

71 

72|56.95!45.31| 
73J56.73  45.94! 

55.7645.55: 
56.53:46.19 

55.5645.80 
56.3346.43 

55.36 
56.13 

46.04 
46.68 

72 
73 

7457.5146.57 

57.3146.82 

57.1047.07 

56.89 

47.32 

74 

7558.2947.20 

58.08  47.45 

57.87:47.71 

57.66^47.96 

75 

76  59.06  47.83 

58.8548.09 

58.6448.34 

58.4348.60 

76 

7759.8448.46 

59.6348.72: 

59.4248.98 

59.2049.24 

77 

7860.6249.09 

60.40  49.35 

60.19J49.61 

59.97 

49.88 

78 

7961.3949.72 

ei.is^g.gs 

60.9650.25, 

60.74 

50.52 

79 

80 

62.1750.35 

61.9550.62 

61.7350.89 

61.51 

51.16 

80 

81 

62.95  50.97 

62.7351.25 

62.5051.52 

62.28'51.79 

81 

82  63.73  51.60 

63.5051.88 

63.27!52.16 

63.0452.43 

82 

83  64.50  52.23 

64.2752.51 

64.04'52.79 

63.81153.07 

83 

84:65.28  52.861  65.05;53.  15 

64.8253.43 

64.58;53.71 

84 

85  66.06  53.49 

65.82'53.78 

65.59  54.07J 

65.3554.35 

85 

8666.83,54.12 

66.6054.41 

66.3654.70 

66.1254.99 

86 

87  67.61  54.75;  67.37 
88j68.3955.38;68.15 

55.05 
55.68 

67.1355.34! 
67.9055.97 

66.8955.63 
67.6656.27 

87 
88 

89 

69.17 

56.01 

68.92 

56.32 

68.67 

56.61 

68.4356.91 

89 

90  69.94 

56.64 

69.70 

56.94 

69.4557.25 

69.20  57.55 

90 

91 
92 

70.72 
71.50 

57.27  70.47 
57.90:  71.24 

57.58 
58.21 

70.2257.88  69.9e'58.19 
70.99  58.52'  70.73  58.83 

91 
92 

93  72.27  58.53 

72.02 

58.84 

71.7659.16  71.5059.47 

93 

24  73.05  59.  16 

72.79 

59.47  172,53  59.79  72.2760.11 

94 

9573.8359.79 

73.5760.11  173.3060.43 

73.0460.75 

95 

96;  74.61 

60.41 

74.34J60.  74  74.0861.06 

73.8161.39 

96: 

97i75.3861.04 

75.12J61.37  74.8561.70 

74.5862.03 

97 

98  76.16:61.67 

75.89 

62.01  75.6262.34 

75.35  62.66 

98 

99  76.94  62.30 

76.66:62.64  76.39  62.97 

76.1263.30 

99 

100  77.71!62.93 

77.44:63.27  !77.16  63.61 

76.8863.94 

100 

! 

i 

Dep.!  Lat. 

Dep. 

Lat.  ! 

Dep. 

Lat. 

Dep.  Lat. 

2 

3 

51   Deg. 

5  02  Deg. 

60JDeg. 

50iDeg. 

a 

118 


TRAVERSE  TABLE. 


B 
a 

40  Deg. 

40JDeg. 

40£Deg. 

,40|Deg. 

5 

ST 

Lat. 

Dep. 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Ji  °-77 

0.64 

0.76 

0.65! 

0.76 

0.65 

0.76 

0.65 

I 

2   1.53 

1.29 

1.53 

1.29 

1.52 

1.30)  1.52 

1.31 

2 

3:  2.30 

1.93 

2.29 

1.94 

2.28 

1.85    2.27 

1.96 

« 

4 

3.06 

2.571  1  3.05 

2.68 

3.04 

2.60    3.03 

2.61 

4 

5 

3.83 

3.21     3.82 

3.23 

3.80 

3.25 

'  3.79 

3.26 

5 

6 

4.60 

3.86 

4.58 

3.88 

4.56 

3.90 

4.55 

3.92 

6 

7 

5.86 

4.50, 

5.34 

4.52 

5.32 

4.55 

6.30 

4.67 

• 

8 

6.13 

5.14 

6.11 

5.17 

6.08 

5.20 

6.06 

5.22 

8 

9 

6.89 

5.79 

6.87 

5.82 

6.84 

6.84 

j  6.82 

5.87 

9 

10 

7.66 

6.43 

7.63 

6.46 

7.60 

6.49 

:    7.58 

6.53 

10 

11    8.43 

7.07 

8.40   7.11 

8.36 

7.14 

i  8.33 

7.18 

11 

12'  9.19 

7.71 

9.16   7.75 

9.12 

7.79 

9.09 

7.83    12 

13,  9.96 

8.36 

9.92 

8.40 

9.89 

8.44 

9.85 

8.491  13 

1410.72 

9.00 

10.691  9.05  10.65 

9.09 

10.61 

9.14    14 

1611.49 
1612.26 

9.64 
10.28 

11.45 
12.21 

9.69  11.41 
10.34  12.17 

9.74  11.36 
10.39:  12.12 

9.79    15 
10.44!  16 

17;  13.02 

10.93 

12.97,  1C.98  12.93 

11.04i  12.88 

11.10;  17 

18  13.79:11.57 

13.74 

11.63  13.69 

11.69;  13.64 

11.75    1& 

19,14.5512.21 

14.50:12.28 

14.45 

12.34;  14.39 

12.40    19 

20  15.32  12.86 

15.2612.92 

15.21 

12.99  15.15 

13.06  20 

21 

16.09 

13.50  16.03:13.57 

15.97 

13.64  15.91 

13.71 

21 

22|  16.85  14.14 

16.7914.21 

16,73 

14.29  16.67 

14.36 

22 

23  17.62 

14.78 

17.55  14.86 

17.49 

14.94!  17.42 

16.01    23 

24  18.39  15.43 

18.32  15.51 

18.25 

15.59  18.18 

15.67   24 

25  19.15  16.07 

19.0816.15 

19.01 

16.24  1S.94 

16.32   25 

26  19.92 

16.71 

19.84  16.80  119.71 

16.89i  19.70 

16.97  i  26 

27,20.6817.36 
28|21.45,18.00 

20.6117.45120.53 
21.37  18.09J  21.29 

17.54  20.45 
18.18121.21 

17.62!  27 

18.281  28 

2922.2218.64 

22.13  18.74i|22.05 

18.83  21.97 

18.93i  29 

30 

22.98  19.28 

22.90  19.38 

22.81 

19.48 

22.73 

19.58 

30 

31 

23.7519.93 

23.6620.03 

23.57 

20.13  23.48 

20.24   31 

32 

24.5120.57 

24.4220.68 

24.33 

20.78,  24.24 

20.89   32 

33 

25.2821.21 

25.1921.32 

25.09 

21.43  25.00 

21.54   33- 

•34 

26.05  21.85 

25.9521.97,25.85 

22.08  25.76 

22.19    34 

35  26.81  22.50 

26.71  22.61  26.61 

22.73  26.51 

22.85   35 

3627.5823.14 

27.4823.26/27.37 

23.38  27.27 

23.50   36 

37  28.34  23.  78^28.24  23.  91  gg.13 

24.03  28.03 

24.15  37 

38 

29.lli24.43 

29.0024.55  28.90 

24.68  28.79 

24.80   38, 

•3929.88;25.07 

29.77  25.20;  29.66 

25.33!  29.54 

25.46 

39 

40|30.64'25.71 

30.5325.84  30.42 

25.98'  30.30 

26.11 

40 

41  31.  41*26.35  31.29  26.49  31.18 

26.63  31.06 

26.78   41 

42  32.17  27.00  32.06  27.14  31.94 
4332.9427.64  32.82  27.78:  S2.7C 

27.28  31.82 
27.93  32.58 

27.42  42 
28.07!  43 

4433.7128.28 

33.58  28.43!  33.46 

28.58J  33.33 

28.72|  44 

45  34.47  28.93 

34.35  29.08!  34.22 

29.23  34.09 

29.37   45 

46,35.24  29.57 

35.1129.72,34.98 

29.87  34.85 

30.03   46 

47  36.00  30.21 

35.87  30.37  i35.74 

30.52  35.61 

30.68   47 

48,36.  77>30.85 

36.6431.01  S6.50 

31.17  36.36 

31.33 

48 

4937.54;31.50 

37.4031.66 

37.26 

31.82i37.12 

31.99 

49 

50 

38.30 

32.14 

38.1632.31 

38.02 

32.47 

37.88 

32.64 

50 

tg 

Dej>. 

^ 
Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

CO 

s 

50  Deg. 

49£Dcg. 

49  1  Deg. 

494iDeg.Q 

TRAVERSE  TABLE. 


119 


g 

40  Deg. 

40£Deg. 

40£Deo. 

40j£Deg. 

o 

en 

Lat 

Dep. 

Lat.JDep. 

Lat 

Dep. 

Lat. 

Dep. 

03 

51 

39.0 

32.78 

38.9232.95 

38.7!r 

33.12 

38.64 

33.29 

51 

52 

39.83 

33.42 

39«S9  !33.  60 

39.54 

33.77 

39.39 

33.94 

52 

K 

40.60 

34.07 

40.45j34.24 

40.3( 

34.42 

40.15 

34.60 

53 

54 

41.37 

34.71 

41.21  34.89 

41.06 

35.07 

40.91 

35.25 

54 

55 

42.13 

35.35 

41.98  35.54 

41.82 

35.72 

41.67 

35.90 

56 

56 

42.90 

36.00 

42.  7< 

36.18 

42.58 

36.37 

42.42 

36.55 

56 

5? 

43.66 

36.64 

43.50 

36.83 

43.34 

37.02 

43.18 

37.21 

57 

58 

44.43 

37.28 

44.27 

37.48 

44.10 

37.67 

43.94 

37.86 

58 

59 

45.20 

37.92 

45.03138.12 

44.86 

38.32 

44.70 

38.51 

58 

60 

45.96 

38.57 

45.7938.77 

45.62 

38.97 

45.45 

39.17 

60 

61 

46.73 

39.21 

46.5639.41 

46.38 

39.62 

46.21 

39.82 

61 

62 

47.49 

39.85 

i7.32  40.06 

47.15 

40.27 

46.97 

40.47 

62 

63 

48.26 

40.50 

48.0840.71 

47.91 

40.92 

47.73 

41.12 

63 

64 

49.03 

41.14 

48.85  41.35 

48.67 

41.56 

48.48 

41.78 

64 

63 

49.79 

41.78 

49.61  42.00 

49.43 

42.21 

49.24 

42.43 

65 

66 

&0.56 

12.42 

50.3742.64 

50.  IS 

42.86 

50.00 

43.08 

66 

67 

51.32 

43.07 

51.1443.29 

50.95 

48.51 

50.76 

43.73 

67 

68 

52.09 

43.71 

51.90  43.94 

51.71 

44.16 

51.51 

44.39 

68 

69 

52.86 

44.35 

52.66144.58 

52.4? 

14.81 

52.27 

46.04 

69 

70 

53.62 

45.00 

53.4345.23 

53.23 

45.46 

53.03 

45.69 

70 

71 

54.39 

45.64 

54.19 

45.87 

53.99 

46.11 

53.79 

46.35 

71 

72 

55.16 

16.28 

4.95 

46.52 

54.75 

46.76 

54.54 

47.00 

72 

73 

55.92 

46.92 

5.7247.17 

55.51 

47.41 

55.30 

47.65 

73 

74 

56.69 

47.57 

6.48147.81 

56.27 

48.06 

56.06 

48.30 

74 

75 

i7.45 

48.21 

7.2448.46 

57.09 

48.71 

56.82 

48.96 

75 

76 

58.22 

8.85 

8.0149.11 

57.79 

49.36 

57.57 

49.61 

76 

77 
78 

58.99 
59.75 

49.49 
o0.14 

8.77 
9.53 

49.75! 
50.40 

58.55 
59.31 

50.01 
50.66 

58.33 
59.09 

50.26 
,50.92 

77 

78 

79 

60.52 

0.78 

60.30 

51.04 

60.07 

51.31; 

59.85 

51.57 

79 

80 

61.28 

51.42 

1.06 

51.69 

60.83 

51.96 

60.61 

52.22 

80 

81 
82 

62.05 

62.8-7 

52.07 
2.71 

1.82 
2.59 

52.341  61.59 
52.98162.35 

52.61 
53.25 

61.36 
62.12 

52.87 
53.53 

81 

82 

83 

63.58 

3.35 

63.35 

53.63 

63.11 

53.90 

62.88 

54.18   83 

84 

64.35 

3.99 

4.11 

54.27 

63.87 

54.55' 

63.64 

54.83^  84 

85 

65.11 

4.64 

64.87 

54.92 

64.63 

55.20 

64.39 

55.48   85 

86 

65.88 

,5.28 

5.64 

55.57 

65.39 

55.85 

65.15 

56.14i  86 

87 

66.615 

5.92 

6.40 

56.21 

66.16 

66.50 

65.91 

56.79   87 

88 

67.41 

6.57 

7.16 

56.86 

66.92 

57.15 

66.67 

57.44 

88 

89 

68.18 

7.?,1 

7.93 

57.50 

67-68 

57.80 

67.42 

58.10 

89 

90 

8.94 

7.85 

8.69 

58.15 

68.44 

58.45 

68.18 

58.75 

90 

91 

69.71 

8,49 

9.45 

58.80 

69.20 

59.10 

68.94 

59.40!  91 

92 

70.48 

9.14 

0.22 

59.44 

6».96|69.75 

69.70 

60.05   92 

93 

1.24 

9.78 

0.98J60,09i 

70.72160.40 

70.45 

60.71    93 

94  72.01 
95  72.77 

0.42 
1.06 

1.74 
2.51 

60.74 
61.38 

71  .48161.05 
7-2.2461.70 

71.21 
1.97 

61.361  94 
62.01    95 

96 

73.54 

1.71 

3.27 

62.03 

73.00,62.35 

72.73 

62.66   96 

97 

74.31 

2.35 

4.03  62.67 

73.76J63.00 

73.48 

JS.32 

97 

98 

75.07 

2.99 

4.80|63.32 

74.52:63.65 

74.24 

63.97 

98 

99 

75.84 

3.64 

5.5663.97 

75.28164.30 

5.0(1 

V4.6?, 

99 

100 

76.60 

64.28 

6.3264.61 

76.04 

64.94 

5.76 

55.28 

100 

•*J 
» 

Dep. 

Lat. 

>ep.  1  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

« 

5 

50  Deg.l 

49|De<r. 

49£Deg.! 

49JDesr.< 

=r 

TRAVERSE  TABLE. 


b 

41   Deg 

41iDeg. 

41iDeg. 

41£Deg. 

0 

pi 

Lat.  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

£ 

i 

0.75 

0.66 

0.75 

0.66 

0.75 

0.66 

0.75 

0.67 

1 

2 

1.51 

1.31 

1.50 

1.32 

1.60 

1.33 

1.49 

1.33 

c 

3 

2.26 

1.97 

2.26 

1.98 

2.25 

1.99 

2.24 

2.00 

£ 

4 

3.02 

2.62 

3.01 

2.64 

3.00   2.65 

2.98 

2.66 

t 

5 

3.77 

3.28 

3.76 

3.30  i  3.74   3.31 

3.73 

3.33 

5 

6 

4.53 

3.94 

4.51 

3.961  1  4.49 

3.98 

4.48 

4.00 

6 

7 

5.28 

4.59 

5.26 

4.621  5.24 

4.64 

5.22 

4.66 

1 

8 

6.04 

5.25 

6.01 

5.27 

5.99 

5.30 

5.97 

5.33 

8 

9 

6.79 

5.90 

6.77 

5.93 

6.74 

5.96 

6.71 

5.99 

9 

10 

7.55 

6.56 

7.52 

6.59 

7.49 

6.63 

7.46 

6.66 

10 

11 

8.30 

8.27 

7.25 

8.24 

7.29 

8.21 

7.32 

11 

12 

9.06 

7.'87 

9.02 

7.91 

8.99 

7.95 

8.95 

7.99 

12 

13 

9.81 

8.53 

9.77 

8.57 

9.74 

8.61 

9.70 

8.66 

13 

14 

10.57 

9.18 

10.53 

9.23 

10.49 

9.28 

10.44 

9.32 

14 

15 

11.32 

9.84 

11.28 

9.89 

11.23 

9.94 

11.19 

9.99 

15 

16 

12.08 

10.50 

12.03 

10.55 

11.98 

10.60 

11.94 

10.65 

16 

17 

12.83 

11.15nl2.78 

11.21 

12.73 

11.26 

12.68  11.32 

17 

18 

13.58 

11.81  13.53 

11.87 

13.4811.93 

13.4311.99 

18 

19 

14.34 

12.47  14.28i  12.53 

14.23!  12.59 

14.18112.65 

19 

20 

15.09 

13.12  15.04 

13.19 

^4.9813.25 

14.92  13.32 

20 

21 

15.85 

13.78 

15.79 

13.85 

15.73  13.91 

15.67 

13.98 

21 

22 

16.60 

14.43 

16.54:14.51 

16.48,14.581  16.41  14.65 

22 

23 

17.36 

15.09 

17.29 

15.16 

I17.23I15.24  17.16  15.32 

23 

24 

18.11 

15.75J  18.04 

15.82 

i  17.97  15.90 

17.91)15.98 

24 

25 

18.87 

16.40  18.80  16.48  18.72 

16.57 

18.6516.65 

25 

26 

19.62 

17.06  19.55  17.14i  19.4717.23  19.40jl7.31 

26 

27 

20.38  17.71 

20.30  17.SOJ  20.22  17.89  20.1417.98 

27 

?8 

21.13  18.37 

21.0518.46 

20.97 

18.56 

20.89  18.64 

28 

29 

21.89il9.03 

21.8019.12 

21.72 

19.22  21.64  19.31 

29 

30 

22.6419.68 

22.5619.78  22.47 

19.88 

22.38 

19.98 

30 

31 

23.4020.34 

23.31  20.44  (23.22 

20.54 

23.13J20.64 

31 

32 

24.15  20.99!  24.06  21.10  23.97121.20:23.87  21.31 

32 

3324.91  21.65;  24.81  21.76J  24.72l21.87'  24.62  21.97 

33 

34  25.66  22.31  25.56  22.421  25.46  22.53  J25.37  22.64 

34 

35 

36 

26.41  22.96,  26.31  23.08!  26.21  23.19  '26.lli23.31 
?7.  1  7  23.  62  i  27.07  23.  74;  26.96123.85  |26.86'23.97 

35 
36 

37 

38 

27.92 
28.68 

24.27:  27.82  24.40  27.71  24.52  J27.60  24.64 
24.93  128.57  25.06'  28.46  25.18  i28.35  25.30 

37 

S8 

39 

29.43 

25.59  29.3225.71  29.21 

25.84,  29.10125.97 

39 

40 

30.19 

26.24:  30.07  26.37  29.96 

26.50 

29.84J26.64 

40 

41  30.94 

26.90  |30.83  27.03  30.71  27.17  30.59  27.30 

41 

4231.70 

27.55  31.58 

27.69  31.4627.83  31.3327.97 

42 

4332.45 
4433.21 

28.21 

28.87 

32.33  28.35  32.21  28.49  32.08  28.63 
33.0829.01  32.95:29.16  32.83!29.30 

43 
44 

45  33.96 

29.52!  33.8329.67:33.7029.82  33.57.29.97 

45 

46  34.72 

30.18  34.58  30.33  34.45  30.48,  34.32  30.63 

46 

47  35.47 

30.83  35.3430.99  35.20J31.  14  35.0631.30 

47 

48 

36.23 

31.49!  36.0931.65!  35:95:31.81  35.81  31.96 

48 

49 

36.98 

32.15:36.8432.31 

36.  70  32.4?;  |36.56  32.63 

49 

50 

37.74 

32.80 

37.5932.97 

37.4533.13 

37.3033.29 

50 

tl" 

Dep. 

LaT 

Dep. 

Lat. 

Dep.    Lat. 

Dep.  Lat. 

5" 

| 

49  Deg. 

48£Deg. 

48iDeg.i|4SiDeg. 

I 

TRAVERSE  TABLE. 


g 

41   Deg. 

41jDeg. 

4UDeg.  41|Deg.  „ 

1  ST. 

r 

Lat. 

Dep. 

Lat.JDcp. 

Lat. 


Dep. 

Lat. 

Dep.j  ft 

51!38.4933.46 
5239.2434.12 
5340.0034.77 

38.34!33.63 
39.10l34.29 
39.85j34.95 

'38.2033.79 
38.95  34.46 
39.6935.12 

38.05 
38.79 
39.54 

33.96  ~51 
34.63    52 
35.29    53 

5440.7535.43 

40.60'35.60 

40.44;35.78 

40.2935.96   54 

5541.5136.08 

41.3536.26 

41.1936,44 

4l.03l36.62i  55 

56  42.26  36.74 

42.1036.92 

41.9437.11 

41.7837.29   56 

57  43.02  37.40  42.85J37.58 

42.6937.77 

42.5337.96   57 

58^3.  77  38.05  43.61:38.24 

43.4438.43 

43.27'38.62   58 

59  44.53138.  71 

44.36i38.90 

44,19^39.09 

44.0239.29i  59 

60  45.28  39.36 

45.11J39.56 

44.94:39.76 

44.76,39.95   60 

6146.0440.02 

45.86'40.22 

!45.69'40.42 

45.5140.62   61 

6246.79 

40.68 

46.61140.88 

46.4441.08 

46.2641.28   62 

6347.55 

41.33 

47.37!41.54 

47.1841.75 

47.0041.95!  63 

6448.30 

41.99 

48.12!42.20 

47.93  42.41 

47.75,42.62]  64 

65  49.06 

42.64 

48.87:42.86 

48.68:43.07 

48.49  43.281  65 

6849.8143.30 

49.62143.52 

49.4343.73 

49.2443.95   66 

67  50.57  43.96 

50.37'44.18 

50.  18  44.40 

49.99144.61!  67 

6851.32'44.61 

51.1344.84 

50.93  45.06 

50.  7345.28!  68 

69 

52.07 

45.27 

51.884.5.49 

51.68 

45.72 

51.48 

45.95!  69 

7052.83|45.92 

52.63:46.15 

52.4346.38 

52.2246.6l|  70 

I 

. 

^^_  '  L   _ 

_ 

-     _     J 

7153.5846.58 

53.3846.81 

53.1847.05 

52.97  47.281  71 

72  54.34  47.24 

54.1347.47  53.9247.71 

53.72l47.94   72 

7355.09!47.89 

54.8848.13 

54.67  48.37 

54.4648.61    73 

74  55.85  48.55 

55.6448.79 

'55.42  49.03 

55.2149.28    74 

7556.6049.20 

56.39  49.45 

56.1749.70 

55.9549.94    75 

76  57.36  49.86 

57.1450.11 

56.9250.36 

56.7050.61 

76 

77  58.11  50.52 

57.8950.77 

57.6751.02 

57.4551.27    77 

7858.8751.17 

58.6461.43 

58.4251.68 

58.1951.94    78 

7959.6251.83 

59.40  52.09 

59.1752.35 

58.9452.60   79 

80  60.38  52.48 

60.1552.75 

59.92  53.01 

59,6853.27 

80 

8l'«1.13'53.14 

60.9053.41 

60.6753.67 

60.43  53.941  81 

8261.8953.80 

61.65  54.07 

61.41 

54.33 

61.1854.60 

82 

8362.6454.45 

62.4054  73 

62.1655.00 

61.9255.27 

83 

8463.4055.11 

63.1555.38  62.91 

55.U6 

62.6755.93 

84 

8564.1555.76 

63.91  56.04 

63.6(i  56.32 

63.41  56.C.O 

85 

86  64.90,56.42 

64.66  56.70 

64.41 

58.99 

64.1657.27 

86 

87  65.66  57.08 

65.41  57.36 

65.1657.65 

64.91 

57.93 

87 

8866.4157.73 

66.1658.02 

65.91 

58.31 

65.65 

58.60 

88 

8967.17158.39 

66.91  58.68 

66.6658.97 

66.4059.26 

89 

90 
91 

67.92J59.05 

63.6859.70 

67.67  59.34  ;67.41J59.  64 
68.42  60.00  :68.  15  60.30 

67.1559.93 
67.8960.60 

90 
91 

92  69.43i60.36 

69.1760.66 

68.9060.96 

68.64 

61.26 

92 

93j70.19 

61.01 

69.92  61.32 

69.6561.62 

69.38 

61.93 

93 

9470.94 

61.67 

70.6761.98 

;70.40  62.29 

70.13 

62.59   94 

9571.7062.33 

71.4362.64 

71.1562.95 

70.88!63.26 

95 

96 

72.45  62.98 

72.1863.30  71.90163.61 

71.6263.92 

96 

97 

73.21 

63.64 

72.93  63.96 

72.6564.27 

72.3764.59 

97 

98 

73.96 

64.29 

73.6864.62 

73.4064.94 

73.11  65.26 

98 

99 

74.72 

64.95 

74.43  65.28 

|74.  15  65.60 

73.8665.92 

99 

100 

75.47 

65.61 

75.1865.93 

74.90;66.26 

74.61 

66.59 

100 

;r 

Dep. 

Lat. 

Dep.  Lat. 

! 

Dep. 

Lat. 

Dep. 

Lat. 

—  — 

t 

CO 

S 

49 

Deg 

k^Dec.  48'  Deg.  48fDes;. 

«, 

TRAVERSE  TABLE, 


g 

42  Dego 

42fDeg. 

42£Deg. 

42^  Deg. 

o 

f 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

ST 

i 

0.74 

0.67 

0.74 

0.67 

0.74 

0.68 

0.73 

0.68 

2 

1.49 

1.34 

1.48 

1.34 

1.47 

1.35 

1.47 

1.36 

2 

3 

2.23 

2.01 

2.22 

2.02 

2.21 

2.03 

2.20 

2.04 

3 

•   4 

2.97 

2.68 

2.96 

2.69 

2.95 

2.70 

2.94 

2.72 

4 

& 

3.72 

3.35 

3.70 

3.36 

3.69 

3.38 

3.67 

3.39 

5 

6 

4,46 

4.01 

4.44 

4.03 

4.42 

4.06 

4.41 

4.07 

6 

7 

5.20 

4.68 

5.18 

4.71 

5.16 

4.73 

5.14 

4.75 

7 

8 

5.95 

5.35 

6,92 

5.38 

5.90 

5.40 

6.87 

5,43 

8] 

'  9 

6.69 

6.02 

6.66 

6.05 

6.64 

6.08 

6.61 

6.11 

10 

7.43 

6.69 

7.40 

6.72 

7.37 

6.76 

7.34 

6.79 

10 

11 

8.17 

7.36 

8.14 

7.40 

8.11 

7.43 

8.08 

7.47 

It 

12 

8.92 

8.03 

8.88 

8.07 

8.65 

8.11 

8.81 

8.15    12 

13 

9.66 

8.70    9.62 

8.74 

9.58 

8.78 

9.55 

8.82    13 

1410.40 

9.37  10.36 

9.41 

10.32 

9.46 

10.28 

9.50!  14 

1511.15 

10.04  11.10 

10.09 

11.06 

10.13 

11.01 

10.18 

15 

.16  11.89!  10.71 
17  12.63!  11.38 

11.84 
12.58 

10.76 
11.43 

11.80 
12.53 

10.81 
11.48 

11.76 

12.48 

10.86 
11.54 

16 
17 

1813.38 

12.04 

13.32 

12.10 

13.27 

12.16 

13.22 

12.22 

18 

19 

14.12 

12.71 

14.0612.77 

14.01  i  12.84 

13.95  12.90 

19 

* 

14.86 

13.38 

14.8013.45 

14.7513.51 

14.69 

13.68 

20 

21 

15.6114.05 

15.5414.12 

15.48114.19 

15.4214.25 

21-. 

22il6.35  14.  72 

;16.2j8 

14.79 

16.22;  14.86 

16.1614.93   22 

•  2317.09 

15.39 

17.02 

15.46 

16.96  15.54 

16.89  15.61   23 

2417.84:16.06 

17.77 

16.14 

17.69 

16.21 

17.6216.29   24 

25  18.58 

16.73 

18.51 

16.81 

18.43  16.89 

18.36 

16.97 

25 

26  19.32  17.40 

19.25 

17.48 

19.17 

17.57 

19.09  17.65!  26 

27  20.06 

18.07 

19.9918.15 

19.91 

18.24 

19.83 

18.33'  27 

28(20.81 

18.74 

20.73 

18.83 

20.6418.92 

20.5619.01    28 

29J21.55  19.40 

21.47  19.50 

21.38:19.59 

21.30 

19.69   29 

so 

22.2920.07 

22.2120.17 

22.1220.27 

22.0320.36!  30 

Ti 

23.0420.74 

22.9^20.84 

22.8620.94 

22.7621.04!  31 

3223.7821.41 
3324.5*22.08 

23.6921.52i 
24.4322.19; 

23.5921.62 
24.33  22.29 

23.5021.72   32 
24.2322.40   33 

3425.2722.75 

25.1722.86  25.0722.97 

24.9723.08   34 

35  2?.01  23.42 

25.91  23.53  |25.80  23.65 

25.7023.76   35 

36 

26.7624.09 

26.65  24.21  126.54  24.32 

26.4424.44   36 

3727.5024.76 

27.39  24.88  ;27.28  25.00 

27.1725.12   37 

38  28.24  25.43 
S9  28.98  26.  10 

28.13  25.55  |28.02  25.67 
28.8726.22  28.7526.35 

27.9025.79   38 
28.6426.47    39 

4029.7326.77 

29.61  26.89  29.49  27.02 

293727.15  40 

41:30.4727.43 

30.3527.57  30.2327.70 

30.1127.83   41 

4231.2128.10 

31.0928.24  30.9728.37 

30.8428.51   42 

4331.9628.77 

31.8328.91  131.70  29.05 

31.5829.19   43 

44  32.  70  29.44;  32.57  29.58  32.4429.73  32.3129.87   44 

45  33.44  30.  1  1  33.31  30.26  33.  18  30.40!  33.04  30.55   45 

4634.1830.78  34.0530.93  33.9131.08  33.7831.22   46 

47,34.93  31.45 

34.79  31.60  134.65  31.75 

34,61 

31.90   47 

4835.6732.12  35.5332.27  35.3932.43 

35.2532.58  48 

49  36.41  32.79  36.27  32.95  36.  13  33.  10 

35.9833.26   49 

50 

37.16  33.46^  37.01  33.62  |36.8G  33.78 

SK.  72  33.94   50 

« 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.  ^ 
.2 

5  48  DegJkTjDegJ^Deg. 

47^1 

TRAVERSE  TABLE. 


123 


42   Deg. 

|42jDeg. 

42^Deg. 

42  1  Deg. 

g 

Lat. 

Dep. 

Lat.  j  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

r 

51  37.90 

34.13 

37.7534.29 

37.60  34,46! 

37.45 

34.62 

51 

5238.64 

34.79 

38.49:34.96 

:38.34i35.13 

38.  18135.30!  52 

63  39.39J35.46 

39.23135.64 

139.08,35.8  1 

38.92)36.98   53 

54  40.  1338.13 

39.97j36.31 

39.8136.48, 

39.65j36.66l  54 

6540.8736.80 

40.7136.98 

40.5537.16 

40.39:37.33   55 

56  41.62137.47 
5742.3638.14 

41.4537.65 
42.19138.32 

41.29  37.83'  41.  12  38.01!  56 
42.02,38.51  41.8638.69   57 

5843.10l38.81 

42.9339.00 

42.7639.18 

42.5939.37   58 

59  43.85J39.48 
60j44.59i40.15 

43.67139.67 
44.41  40.34 

43.50  39.86 
44,24,40.54 

43.3240.05   59 
44.0640.73   60, 

__^ 

61  !45.33  40.82 

45.15 

41.01 

44.9741.21 

44.79  41.4l|  61 

6246.0741.49 

45.89 

41.69 

45.7141.89 

45.5342.09   62 

6346.82(42.16 

46.63 

42.36 

46.45  42.56 

46.2642.76   63 

6447.56i42.82 

47.37 

43.03 

47.1943.24 

47.00  43.441  64 

65  48.30  43.49 

48.11 

43.70  47.9243.91 

47.7344.12    65 

66  49.05 

44.16 

48.86 

44.38 

48.66  44.59 

48.47  44.80 

66 

6749.79 
68  50.53 

44.83  49.69 
45.50  50.33 

45.05 
45.72 

49.40  45.26 
50.1346.94 

49.20 
49.93 

46.4&  67 
46.16   68 

6951.28 

46.17 

51.07 

46.39  50.8746.62 

50.67 

46.84 

69 

7052.02 

46.84 

51.82 

47.07 

5).  61 

47.29 

51.40 

47.52 

70 

71 

52.76 

47.51 

52.56 

4J.74!  52.35 

47.97 

52.14 

48.19 

71 

7253.51 

48.18 

53.30 

48.41 

53.08 

48.64 

62.87 

48.87 

72 

73|54.25 

48.85 

54.04 

49.08 

53.82 

49.32 

63.61 

49.55 

73 

7454.99 

49.52 

54.78 

49.76 

54.  6C 

49.99 

54.34 

50.23 

74 

7555.74 

50.18  55.52 

50.43 

55.30 

50.67 

55.07 

50.91 

75 

7656.4S 

50.86 

66.26 

51.  U) 

56.03 

51.34 

55.81 

51.69 

76 

7757.22 

51.52 

;57.00 

51.77 

56.77 

52.02 

56.64 

52.27 

77 

7857.97 

52.19 

167.74 

52.44 

167.51 

52.70 

57.28 

52.95 

78 

79J58.71 

52.86 

58.48 

53.12 

58.24  53.37 

58.01  53.63 

79 

80 

59.45 

63.63 

59.22 

53.79 

58.98 

54.05 

68.75 

54.30 

80 

81 

60.19 

54.20 

59.96 

54.46 

59.72 

54.72 

59.48  64.98 

81 

8260.94 

54.87 

60.70 

55.  13  160.46 

55.40 

60.21  55.66 

82 

8361.68 

55.54 

61.44 

55.81  '61.19 

66.07 

60.9556.34 

83 

8462.4256.21 

62.18 

56.48 

61.93 

56.75 

61.68  57.02 

84 

8563.1756.88 

62.92 

57.15 

62.67  57.43 

62.4257.70 

85 

86  63.91  !67.55 

63.66 

57.82 

63.4L58.10 

63.1558.38 

86 

87  64.65  58.21 

64.40 

58.50 

64.1458.78 

63.89  69.06 

87 

88  65.40  68.88 

65.14 

59.17 

64.8859.45 

64.62  59.73 

88 

8966.1459.55  65.88 
90,66.88i60.22  66.62 

59.84 
60.51 

66.6260.13 
66.35  60.80 

65.35  60.41 
66.09  61.09 

89 
90 

1  ;  

91  '67.63'60.89  67.36 

61.19 

67.09  61.48 

66.8261.77 

91 

9268.3761.56 

68.10 

61.86 

67.8362.15 

67.56  62.46 

92 

9369.1162.23 

68.84 

62.53 

68.57  62.83 

68.2963.13 

93 

94  69.86  62.90 

69.58 

63.20 

69.30  63.51 

69.0363.81 

94 

95  70.60  63.57 

70.32 

63.87 

70.0464.18 

69.76  64.49 

95 

9671.3464.24 

71.06 

64.55 

70.78  64.86 

70.4965.16 

96 

97  72.08  64.91 

71.80 

65.22 

71.52  65.63 

71.2365.84   97 

98  72.83  65.57 

72.5465.89 

72.25  66.21 

71.9666.52    98 

99 

73.57  66.24 

73.28  66.56 

72.99  66.88 

72.7067.20 

99 

100 

74.31  66.91 

74.02 

67.24 

73.73  67.56 

73.43  67.88 

100 

99 

Uep.  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

IT 

»M 

48  Deg. 

4743  Deg. 

47]  Deg. 

47]  Deg. 

5 

124 


TRAVERSE  TABLE. 


g 

43  Deg. 

43],Deg. 

43^t)eg.  43»  Deg.  ^ 

F 

Lat. 

Dep. 

H 

Dep. 

Tat? 

Dep. 

ia 

Dep. 

r 

j 

0.73 

0.68 

0.73 

0.69 

0.73 

0.69 

'  0.72 

0.69 

i 

2 

1.46 

1.36 

1.46 

1.37 

1.45 

1.38 

i  1.44 

1.38 

2 

3 

2.19 

2.05 

2.19 

2.06 

2.18 

2.07 

2.17 

2.07 

3 

4 

2.93 

2.73 

2.91 

2.74 

2.90 

2.75 

2.89 

2.77 

4 

5 

3.66 

3.41 

3.64 

3.43 

3.63 

3.44 

3.61 

3.46 

5 

6 

4.39 

4.09 

4,37 

4,11 

:  4.35 

4.13 

4.33 

4.15 

6 

7 

5.12 

4,77 

5.10 

4.80 

5.08 

4.82 

5.06 

4.84 

7 

8 

5.85 

5.46 

!  5.83 

5.48 

i  5.80 

5.51 

5.78 

5.53 

8 

9   6.58 

6.14 

6.56 

6.171    6,53 

6.20 

6.50 

6.22 

9 

10|  7.31 

6.82 

7.28 

6.85  j  7.25   6.88 

7.22 

6.92 

10 

"Til  8.04 

7.50 

i  8.01 

7.541    7.93 

7.57 

7.95 

7.61    11 

12   8.78 

8.18 

8.74 

8.221    8.70 

8.26 

8.67 

8.30 

12 

13   9.51 

8.87 

9.47 

8.91 

9.43 

8.95 

9.39 

8.99 

13 

14  10.24 

9.55 

10.20 

9.59 

10.16 

9.64 

10.11 

9.68 

14 

15  10.97 

10.23 

10.93 

10.28 

10.88  10.33 

10.84 

10.37 

15 

16111.70110.91 

11.65 

10.96 

11.61 

11.01 

11.5611.06 

16 

17112.4311.59 

12.38 

11.65 

12.33  11.70 

12.2811.76 

17 

18 
19 

13.1612.28 
13.90  12.96 

13.1112.33 
13.8413.02 

13.06  12.39 
13.7813.08 

13.0012.45 
13.72il3.14 

18 
19 

20 

14.63 

13.64 

14.57J13.70;  14.51 

13.77 

14.45  13.83 

20 

21 

22 

15.36  14.32 
16.0915.00 

15.30 
16.02 

14.39 
15.07 

15.4314.46 
15.96  15.14 

15.1714.52 
15.89  15.21 

21 

22 

23  16.82  15.69 

16.  75  !  15.  76 

16.68 

15.83 

16.61 

15.90 

23 

24|  17.55  16.37 

17.4816.44 

17.41 

16.52 

17.3416.60 

24 

2518.2817.05 

18.21 

17.13 

18.1317.21 

18.06  17.29 

25 

2619.0217.73 

18.9417.81 

18.86 

17.90 

18.7817.98 

26 

27i9.7518.41 

19.67 

18.50 

19./>9 

18.59 

19.5018.67 

27 

2820.4819.10 

20.3919.19 

20.31 

19.27 

20.23  19.36 

28 

29,21.21  19.78 

21.12  19.87 

21.04 

19.96 

20.95  20.05 

29 

3021.9420.46 

21.85  20.56 

21.7620.65 

21.67  20.75 

30 

1 

______ 

______ 

. 



3122.6721.1422.5821.24 

22.49  121.34 

22.3921.44 

31 

3223.4021.82 

23.31 

21.93 

23.21 

22.03 

23.12 

22.  13 

32 

33  24.  13i22.51 

24.04  22.61 

23.9422.72 

23.8422.82 

33 

34  24.87123.  19 

24.7623.30 

24.6623.40  24.5623.51 

34 

35|25.60  23.87 

25.49  23.98 

25.3924.09 

25.2824.20 

35 

36  26.33  24.55 

26.2224.67 

26.11 

24.78 

26.0124.89 

36 

37;27.06 

26.23 

26.95  25.35 

26.84125.47 

26.7325.59 

37 

38127.79 

25.92 

27.68  26.04 

27.5626.16  27.4526.28 

38 

3928.52 

26.60 

28.41  26.72 

28.29:26.85 

28.1726.97 

39 

40 

29.25 

27.28 

^9.1327.41 

29.01 

27.53 

28.8927.66 

40 

41 

29.99 

27.96 

29.8628,09)29,7428.22 

29.62!2.8.35 

41 

42 

30.72 

28.64 

130.  59  28.  78 

;30.47  28.91 

30.34  29.04 

42 

43 

31.45 

29.331131.3229.46 

31.19(29.60 

31.0629.74 

43 

44132.18 

30.01 

!32.0530.15 

31.9230.29 

31.7830.43 

44 

45J32.91 

30.69 

!32.7830.83 

32.64'30.98!32.5131.12 

45 

46:33.6431.37 

33.5131.52 

33.3731.66 

33.2331.81 

46 

47;34.-S7!32.05 

34.2332.20  34.0932.35 

33.95  32.50 

47 

4835.10 

32.74 

34.96  32.89  ;34.82'33.04 

34.6733.19 

48 

49  35.84 

33.42 

35.69  33.57 

35.54i33.73 

35.4033.88 

49 

50 

36.57 

34.10 

;36.42  34.26  36.27 

34.42 

36.1234.58 

50 

*i 

Dep. 

Lat. 

|De7 

Lat. 

IDep. 

Lat. 

JDep. 

Lat. 

cc 

S 

47  Deg. 

462Deg.!|46_rDeg.  '46j;Deg. 

s 

TRAVERSE  TABLE. 


125 


^'43  Deg 

43^  Deg. 

43fDe* 

43^  Deg 

s 

rJLat 

Dep 

Lat 

Dep. 

Lat. 

Dep 

Lat 

Dep 

5 

5l'37.3C 

34.78 

37JL5 

34.94 

36.99 

35.1 

36.84 

S5.21 

51 

5238.03 

35.46 

37.'8* 

35.63 

37.7235.7 

;37.56 

35.96 

52 

5338,76 

36.15 

38.6C 

36.31 

38.4436.4 

;38.29 

36.65 

53 

5439.49 

36.83 

39.32 

*7.00 

39.1737.1 

'39.01 

37.34 

54 

6540.22 

37.5 

40.06 

37.69 

39.9037.86 

j39.73 

38.03 

55 

56  40.96 

38.19 

40.78 

38.37 

40.62  38.55 

40.45 

38.72 

56 

5741.69 

38.87 

41.52 

39.06 

41.3589.24 

41.17 

39.42 

57 

5842.42 

39.56 

42.25 

39.74 

42.0739.92 

141.90 

40.11 

58 

5943.15 

40.24 

42.97 

40.43 

42.8040.61 

142.62 

40.80 

59 

6043.88 

40.92 

43.70 

41.11 

43.52  41.30 

43.34 

41.49 

60 

6l'44.61 

41.60 

44.43 

41.80 

44.25*41.99 

44.06 

42.18 

61 

6245.34 

42.28 

45.16 

42.48 

44.97  42.68 

,44.79 

42.87 

62 

63  46.08 

42.97 

45.89 

43.17 

45.7043.37 

45.51 

43.57 

63 

6446.81 

43.65 

46.62 

43.86 

46.42  44.05 

146.23 

44.26 

64 

6547.64 

44.33 

47.34 

44.54 

47.1544.74 

46.95 

44.95 

65 

6648.27 

45.01 

48.07 

45.22 

47.87  45.43 

47.68 

45.64 

66 

6749.00 

45.69 

48.80 

46.91 

48.8046.12 

48.40 

46.33 

67 

6849.73 

46.38 

49.53 

46.59 

49.3346.81 

49.12 

47.02 

68 

69  50.46 

47.06 

50.26 

47.28 

50.05  47.50 

49.84 

47.71 

69 

70J51.19 

47.74 

50.99 

47.96 

50.7843.18 

50.57 

48.41 

70 

71!51.93 

48.42 

51.71 

48.65^ 

51.5048.87 

51.29 

49.10 

71 

72  52.66 

49.10 

52.44 

49.33 

52.2349.66 

52.01 

49.79 

72 

73  63.39 

49.79 

53.17 

50.02  152.95  50.25 

52.73 

60.48 

73 

7454.12 

o0.47i 

53.90 

50.  70.  '53.68  50.94 

53.45 

51.17 

74 

7554.85 

ol.lS 

54.63 

51.39i54.405l.63 

54.18 

51.86 

75 

7665.5fc 

ol,83 

55.36 

52.07  166.  13  52.31 

54.90 

52.65 

76 

77  56.3] 

j2.i>] 

56.08 

52.76  55.8553.00 

55.62 

53.25 

77 

78J57.05 

j3.20 

56.81 

53.44  56.5853.69 

56.34 

53.94 

78 

7957.78 

o3.88 

57.54 

54.13:57,3054.38 

57.07 

54.63 

79 

8058.51 

4.66 

8.27 

54.81:58.0355.07 

57.79 

55.32 

80 

81  59.24 

5.24 

9.00 

j5.60  58.7655.76 

58.51 

56.01 

81 

82  69.97 

5.92 

9.73 

56.18  59.4856.45 

59.23 

66.70 

82 

8360.70 

6.61 

0.45 

56.87  60.2157.13 

59.96 

57.40 

83 

84|61.43 

7.29 

1.18 

7.  56160.  93  57.  82 

60.68 

58.09 

84 

85'62.17 

7.97 

1.91 

58.241  61.66  58.51 

61.40 

58.78 

85 

8662.90 

8.65 

2.64 

58.93J  62.38  69.20 

62.12 

59.47 

86 

87  63.63 

9.33 

3.37 

59.61  63.11  59.89 

62.85 

60.16 

87 

88:64.36 

0.02 

4.10 

60.301  63.83  60.58 

63.57 

60.85 

88 

89J65.09 

SO.  701 

4.82 

60.98  64.5661.26 

64.29 

61.54 

89 

90J65.82 

1.38 

5.55 

61.67 

65.2861.95 

65.01 

6224 

90 

9li66.55 

2.06 

6.28 

62.35 

86.0162.64 

65.74 

62.93 

91 

92<67.28 

2.74 

7.01 

63.04| 

66.73  63.33 

66.4663.62 

92 

93;68.02 

63.43 

7.74 

63.72 

67.46,64.02 

67.18:64.31 

93 

9468.75 

4.11 

8.47 

64.41 

68.1964.71 

67.90:65.00 

94 

95169.48 

4.79 

9.20 

65.09 

88.91  65.39 

o8.6265.69 

95 

96170.21 

5.47 

9.92 

65.78 

69.6466.08 

9.35  66.39 

96 

97170.94 

6.15 

0.65 

66.46 

70.3666.77 

0.07  67.08 

97 

98  71.67 

6.84 

1.37 

67.15 

71.09  67.46 

0,79  67.77 

98 

99  72.40 

7.62 

2.11 

67.83 

71.816 

8.15 

1.51  68.46 

99 

10073.14 

8.20 

2.84 

68.52 

72.5468.84 

2.24169.15 

100 

Lat. 

Lat. 

U  Dep. 

D 

Lat. 

Dep. 

Lat. 

DepJ 

DepJ 

tZ 

P  47  Deg. 

6|Deg. 

46£Deg. 

46iDeg. 

1 

126 


TRAVERSE  TABLE. 


^44  Deg. 

44^  Deg.  44£Deu. 

44^  Deg 

45  Deg. 

9 

00 

Lat.!  Dep. 

Lat.  Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

X 

«•*• 

1 

0.72'  0.69 

0.72   0.70    0.71 

0.70 

0.7l!  0.71 

0.71 

0.71 

~~1 

2 

1.44    1.39 

1.43    1.40     1.43 

1.40 

1.42 

1.41 

1.41 

1.41 

2 

3 

2.16!  2.08 

2.15   2.09    2.14 

2.10 

2.13 

2.11 

2.12 

2.12J    3 

4 

2.88i  2.78 

2.87   2.79'    2.85 

2.80 

2.84 

2.82 

2.83 

2.83!    4 

5 

3.60j  3.47 

3.58   3.49     3.57 

3.50 

3.55 

3.52 

3.54 

3,54     5 

6 

4.32   4.17 

4.30   4.19    4.28 

4.21 

4.26 

4.22 

4.24 

4.24     6 

7 

5.04    4.86 

5.01   4.88    4.99 

4.91 

4.97 

4.93 

4.95 

4.95     7 

8 

5.75i  5.56; 

5.73   5.58     5.71 

5.61 

5.68 

5.63 

5.66 

5.66'    8 

9! 

6.47   6.25 

6.45   6.28     6.42 

6.31 

6.39 

6.34 

6.36 

6.36 

9 

10; 

7.191  6.95 

7.16   6.98!  7.13 

7.01 

7.10 

7.04 

7.07 

7.07 

10 

M^ 

_  t.   1  _^  _.,_,__, 

—  —           1  1 

__ 

11 

7.91    7.64 

7.88    7.68 

7.85 

7.71 

7.8li  7.74 

7.78 

7.78 

11 

12 

8.63|  8.34 

8.60   8.37 

8.56 

8.41 

8.52 

8.45 

8.49 

8.49 

12 

13 

9.35   9.03 

9.31    9.07     9.27 

9.11 

9.23 

9.15 

9.19 

9.19 

13 

1410.07!  9.73 

10.03   9.77     9.99 

9.81 

9-94 

9.86 

9.90 

9.90 

14 

1510.7910.42 

10.  74  10.47!  10.70  10.51 

10.6,5  10.66 

10.61 

10.61 

15 

1611,51:11.11    11.4611.16  11.41 

11.21111.36 

11.26 

11.31 

11.31 

16 

1712.2311.81   12.1811.86  12.1311.92 

12.0711.97 

12.02 

12.02 

17 

1812.9512.50 

12.89  12.56  12.84  12.62 

12.78 

12.67 

12.73 

12.73 

18 

1913.6713.20 

13.6113.26  13.5513.32 

13.49 

13.38 

13.43 

13.43 

j< 

20114.39  13.89 

14.3313.96  14.26:14.02 

14.20  14.08 

14.14 

14.14 

20 

2ljl5.ll  I4.59i 

15.04  14.65  14.98 

14.72!  14.91 

14.78 

14.85 

14.85   21 

2215.8315.28 

15.76  15.35  15.69 

15.42 

15.62  15.49 

15.56 

15.56   22 

23  16.54  15.98  16.47  16.05;  16.40  16.12i  16.33  16.19 

16.26 

16.26   23 

24  17.26  16.67  17.19  16.751  17.12  16.821  17.04  16.90^16.9" 

16.97   24 

25  17.98  17.37  ,17.91  17.44  17.83  17.52 

17.75  17.60)!  17.68 

17.68   25 

26 

18.70  18.06  118.62  r8.14  18.54 

18.22 

18.46  18.301  18.38 

18.38   26 

27  19.42  18.76  19.34  18.84'  19.26 

18.92 

19.17  19.01 

19.01 

19.09   27 

28  20.14  19.45  :20.06  19.54  19.97119.63 

19.89  19.71 

19.80 

19.80   28 

2920.8620.15  20.7720.24  20.68i20.33 

20.60  20.42 

20.5 

20.51    29 

30,21.58  20.84^21.49  20.93  21.40J21.03 

21.31  21.12 

21.2 

21.21 

30 

31  22.30  21.53  122.21  21.63 

22.11 

21.73 

22.0221.82 

21.92 

21.92|  31 

'3223.0222.23  22.9222.33  22.82122.  43 

22.73  22.53 

22.63 

22.631  32 

33  23.74  22.92  ;23.  64  23.03  23.54  23.  13 

1  23.44  23.23 

23.33 

23.331  33 

34  24.46  23.62;  124.35  23.  72;  24.25'23.83l  24.1523.94  24.04 
3525.1824.31  ;25.07  24.42  24.96i24.53;  24.86  24.64|  24.7o 

24.04 
24.75 

34 
35 

36,25.90  25.01;;25.  79  25.12 

25.68125.23:  25.57  25.34|  25.46 

25.46 

36 

37  26.6225.70  26.5i;  25.8. 

26.39  25.93 

26.2826.05  26.16 

26.16 

37 

38  27.33  26.40  527.22  26.52 

27.  10  26.631  26.  9S 

26.75  26.  S 

26.87 

38 

39  28.05  27.09!  27.94  27.21 

27.82 

27.34 

27.7027.46  27.58 

27.58 

39 

40 

28.  77|27.79|  2S.65  27.91 

28.53 

28.04  28.41  2£.  16  28.28 

28.28 

40 

~4i;29.49  28.48^  '29.37  28.61 
42,30.21  29.  18:30.08  29.31 
43  30.93  29.871  !30.80  30.00 

29.24  28.  74?  29.  12  28.86 
29.96  29.441  29.  83  29.57 
30.67  30.  14J  30.54  30.27 

'28.99 
29.70 
30.4 

28.99 
29.70 
30.41 

41 

42 
43 

4431.6530.56 

131.52  30.70 

31.3830.84 

:  31.  25  30.98 

31.1 

31.11 

44 

45!32.37  31.26 

;32.23  31.40 

32.1031.54 

131.9831.68 

31.82 

31.82 

45 

46^33.0931.95 
47iS3.81  32.65 

^32.9532.10 
J33.67  32.80 

32.81 
33.52 

32.24 
32.94 

i  32.67  32.38 
'33.3833.09 

32.53 

33.23 

32.53 
33.23 

46 
47 

4834.5333.34 

'34.3833.49 

34.24 

33.64 

34,0933.79 

83.94 

33.94  48 

49 

50 

36.25  34.04 
35.9734.73 

35.1034.19 

35.8234.89 

i 

34.95 
35.66 

34.34 
35.05 

34,8034.50 
35.51  35.20 

34.65 
35.36 

34.65   49 
35.36  50 

«j 

Dep.!  Lat. 

Dep.j  Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

j_* 

'          _.  _|    t« 

4£  Deg. 

46£Deg. 

45peg. 

1451  Deg. 

45  Deg.  3 

TRAVERSE  TABLE. 


127 


«44  Deg.  44£Deg.|4 

t4^Deg.  44|Deg. 

45  Deg. 

O 

A   Lat.!  Dep.  ^ 

Lat.  Dep.    Lat.JDep. 

Lat.  Dep. 

Lat.jl 

Dep. 

•""    •  •  . 

» 

~5l  36.69*35.43  36.53  35.59  36.38  35.75  36.2235.90 

36.06  $. 

56.06 

51 

5237.41J36.12  37.2536.29  37.09136.45  36.9336.61 

36.7736.77 

52 

5338.12j36.82  37.9636.98  37.8037.15  37.6437.31 

37.48|37.48 

63 

54  3S.84l37.51  38.6837.68  38.52:37.85  38.35.38.02 

38.18138.18 

54 

55  39.56  38.21  39.40  38.38  39.23  38.55  3S.06  38.72 

38.89'' 

J8.89 

55 

56  40.28i38.90  40.1139.08  39.9439.25  39.7739.4.2 

39.6039.60 

56 

5741.0039.60  40.8339.77  40.6639.95 

40.4840.13 

40.31  ;40.S1 

57 

6841.72J40.29  41.5540.47  41.37:40.65 

41.  19  -40.831  41.01  41.01 

58 

5942.4440.98  42.2641,17  42.08'41.35 

41.9041.64 

41.7241.72 

59 

60;43.  16:41.68  42.98  41.87  42.79 

42.05 

42.61 

42.24 

42.4342.43 

60 

6143.8842.37  43.6942.67  43.51i42.76 

43.32 

42.94 

43.1343.13   61 

6244.6043.07  44.4143.26  44.22J43.46 

44.03(43.65 

43.8443.84 

.62 

6345.32!43.76  45.1343.96  44.93J44.16 

44.  74i|  44.35 

44.55  44.55 

63 

6446.04i44.46  45.8444.66  45.65144.86 

45.4545.06 

45.25  45.25 

64 

65  46.76I45'.1'5  46.5645.36  46.36  4o  56 

46.16j45.76 

45.9645.19 

65 

6647.48J45.85  47.2846.05  47.0746.26 

46.8746.46 

46.67  46.67 

66 

67  48.20146.54  47.99  46.  7a  47.7946.96 

47.58147.  17 

47.38  47.38 

67 

6848.9247.24  48.7147.45  48.50;47.66 

48.29l47.87 

48.08  48.08 

68 

69  49.63147.93 

49.4248.16  49.21(48.36 

49.00  48.58 

48.7948.79 

69 

7050.35:48.63  50.1448.85  49,93 

49.06 

49.71  49.28 

49.5049.50 

70 

71  51.07;49.32 

50.86'49.54 

50.64 

49.76 

50.42l49.98 

50.2050.201  71 

72  51.79!50.02 

51.57150.24 

51.35 

50.47 

61.13 

60,69 

50.91  60.91 

72 

7352.5150.71 

52.29  150.  94 

52.07 

51.17 

51.84 

51.39 

51.6251.62 

73 

7453.2351.40 

53.01j51.64 

52.78 

51.87 

52.55 

52.10 

52.33  52.33 

74 

7553.9552.10 

53.72i52.33 

53.49 

52.57 

53.26J52.80 

53.03  53.03 

75 

7654.6752.79 

54.44,63.03 

54.21 

5327 

53.97 

53.61 

53.7453.74 

76 

77  55.39  53.49 

55.  16i53.  73 

54.92 

53.97 

54.68 

54.21 

54.4554.45   77 

7856.1154.18 

55.87J54.43 

55.63 

54.67 

55.39 

54.51 

55.1555.15 

78 

79  56.83  54.88 

56.59155.  13 

66.35 

55.37 

66.1055.62 

55.86  55,86 

79 

.  80  57.55  55.57 

67.30.55.  82 

_                   |  f  ; 

57.06 

56.07 

56.81 

56.32 

56.57  56.57 

80 

81:58.27  56.27 

58.02J 

57.77 

56.77 

57.52 

57.03 

57.28  57.28 

81 

8258.9956.96 

58.74J57.22 

58.49 

57.47 

•58.24 

57.73 

57.9857.98   82 

8359.71 

57.66 

59.45i57.92 

59.20  58,18 

-58.95 

58.43 

58.6958.69   83 

84  60.42  58.35 

80.17i58.61 

59.91!58.88 

169.66 

59.14 

59.4059.40   84 

8561.14'59.05 

60.89l59.31 

60.63 

59.58  160.37 

59.84 

60.  10  -60.10  85 

8661.8659.74 

61.6060.01 

61.34 

60.28 

161.08 

60.55 

60.81 

60.81 

•  8 

'8762.5860.44 

62.3260.71 

62.05 

60.98 

[61.79 

61.25 

61.52 

61.52   87 

8863.30!61.13 

63.0361.41 

62.7761.68 

62.5061.95 

62.23 

62.23-  88 

8964.0261.82 

63.75'62.10 

63.48  62.3S 

163.21  62.66 

62.93 

62.93   89 

90,64.74 

62.52 

64.47  162.80 

64.19 

63.08 

63.92 

63.36 

63.64 

63.64,  90 

M 

65.46 

63.21 

65.1863.50 

6491 

63.78  J64.63  64.07 

64.35 

64.35   91 

9266.1863.91 

65.90  64,20  65.62  64.48 

65.34  64.  Tt 

65.05 

65.05   92 

93  66.90  64.60 

66.6264.89 

66.3365.18 

66.05:65.47 

66.76 

65.76   93 

94  67.62  65.30 

67.33'65.59l 

67.05'65.89 

66.76!66.18 

66.47 

66.47   94 

9568.3465.99 

68.05  66.29 

67.76:66.59 

67.47:66.88 

67.18 

67.18   95 

9.5  69.06  66.69 

68.76.66.99 

68.47 

67.29 

68.18i67.59 

67.88 

67.88 

96 

97'69.78 

67.38 

69.4867.6'J 

69.19 

67.99 

68.89:68.29 

68.59 

68.59    97 

98!70.50 

68.08 

70.2068.38 

69.9068.69 

69.60  68.99 

69.30 

69.30   98 

99 
100 

71.21 
71.93 

68.77 
69.47 

70.91 
71.63 

69.08 
69.78 

70.61 
71.33 

169  39 
70.09 

70.31  69.70 
71.0270.40 

70.00 
70.71 

70.00 
70.71 

89 
100 

to 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

'Lat. 

Dep. 

Lat. 

CO 

*  ~+ 

46  Deg. 

45£Deg. 

45peg. 

4sTDeg. 

45  Deg. 

5 

128  NATURAL  SINES. 

IV.  A  TABLE  of  NATURAL  SINES,  calculated  to  Jive  places  of 
figures,  for  every  Minute* 

NATURAL  SINES  are  Decimals  bearing  the  same  proportion 
to  Unity  or  1  that  the  Sine  of  the  corresponding  number  of 
Degrees  and  Minutes  bears  to  Radius  or  Sine  of  90°.  That  is. 
1  is  assumed  as  the  Nat.  Sine  of  90°,  and  the  Table  calculated 
accordingly. 

Explanation  of  the  Table. 
To  find  the  Natural  Sine  of  any  number  of  Degrees  and  Minutes. 

If  the  degrees  be  less  than  45,  look  for  them  at  the  Top  of 
the  Columns,  and  for  the  Minutes  at  the  left-hand  ;  but  if  more 
than  45,  look  for  them  at  the  Bottom,  and  for  the  Minutes  at  the 
right-hand  ;  under  or  over  the  Degrees  and  against  the  Minutes 
will  be  the  Natural  Sine  required. 

The  reverse  of  this  will  give  the  Degrees  and  Minutes  cor- 
responding to  any  Natural  Sine. 

To  calculate  the  Northing  or  Southing,  fyc.  for  any  Course  and 
Distance,  by  Nat.  Sines. 

Find  the  Nat.  Sine  and  Co- Sine  of  the  Course,  and  into  each 
of  these  multiply  the  Distance  ;  the  Products  will  be  the  Lati- 
tude and  Departure  required. 

EXAMPLE. 

Required  the  Latitude  and  Departure  for  6  Chains  and  22 
Links,  on. a  Course  JV.  38O  27'  W. 

Nat.  Sine  of  38°  27',  0.62183    Nat.  Co-Sine  0.78315: 
6.22  6.22 

124366  156630 

124366  156630 

373098  469890 


3.8677826  4.8711930 

Answer.     Northing  4.87  Westing  3.87 


A  TABLE  OF  NATURAL  SINES. 


129 


0  Deg. 

1  Deg. 

2  Deg.  1  3  Deg. 

4  Deg. 

Nat.  )N.C- 

Nat.  iN.C- 

Nat.:N.C-JNat.N.C~ 

Nat.  N.C- 

M 

Sine  Sine 

Sine  Sine 

Sine  Sine]  Sine 

Sine 

Sinel  Sine 

M 

~0 

30000  UnTtT 

)1745  99985  03490  99939,05234  99863  06976  99756 

~60 

1 

29 

00 

774   84 

519   38 

263 

61  07005 

54 

59 

2 

58 

00 

803   84 

548 

37 

292 

60  034 

52 

58 

3 

87 

00 

632 

83 

577 

36 

321 

58 

063 

50 

57 

4 

11% 

00 

862i   83 

6061   35 

350 

57 

092 

48 

56 

5 

145 

00 

891  1   82 

6351   34 

379 

55 

121 

46 

55 

6 

175 

00 

920|   82 

664   33 

408 

54 

150 

44 

54 

7 

204 

00 

949!   81 

693   32 

437 

52 

179 

42 

53 

8 

233 

00 

978   80 

723   31 

466 

51 

208 

40 

52 

9 

262 

00 

32007   80 

752;   30 

495 

49 

237 

38 

51 

10 

291 

00 

036 

79 

731|   29 

524 

47 

266   36 

50 

11 

320  99999 

065,   79 

810!   27 

553 

46 

295   34 

49 

12 

349   99 

094J   78 

839!   26 

582 

44 

324   31 

48 

13 

378 

99 

123   77 

868   25 

611 

42 

353   29 

47 

14 

407 

99 

152 

77 

897 

24 

640 

41 

332   27 

46 

15 

436   99 

181 

76 

926   23 

669 

39 

411 

25 

45 

16  046599999 

221199976  395599922 

5698  99838 

^744099T27J 

44 

17 

495   99 

240   75 

984,   21 

727 

36 

489 

21 

43 

18 

524 

99 

269 

74 

4013   19 

756 

34 

498 

19 

42 

19 

553 

98 

298 

74 

042   18 

785 

33 

527 

16 

41 

20 

582 

98 

327 

73 

071   17 

814 

31 

556 

14 

40 

21 

611 

98 

356 

72 

100   16 

844 

29 

585 

12 

S9 

22 

640 

98 

385 

72 

129   15 

873 

27 

614 

10 

38 

23 

669 

98 

414 

71 

159   13 

902 

26 

643 

08 

37 

24 

698 

98 

443   70 

188   12 

931 

24 

672 

05 

36 

25 

727 

97 

472 

69 

217   11 

960 

22 

701 

03 

35 

26 

756 

97 

501 

69 

246   10 

989 

21 

730 

0 

34 

27 

785 

97 

530 

€8 

275!   09 

6018 

19 

759  99699 

33 

28 

814 

97 

560 

67 

3041   07 

047 

17 

788 

96 

32 

29 

844   96 

589 

66 

333   06 

076 

15 

817 

94 

31 

30 

873   96 

618 

66 

362)   05 

105 

13 

846 

92 

30 

~3l 

OOSG2  99996 

2647>99965 

0439L99904 

06134 

99812 

07875 

99689 

129 

32 

931 

96 

676 

64 

420J   02 

163 

10 

904 

8 

28 

33 

960 

95 

705 

63 

449   01 

192 

08 

933 

8 

27 

34 

989 

95 

734 

63 

478   00 

221 

06 

962 

8 

26 

35 

01018 

95 

763 

62 

507  99898 

250 

04 

991 

8 

25 

36 

047 

95 

792 

61 

536 

97 

279 

03 

08020 

7 

24 

37 

076 

94 

821 

60 

565 

96 

308 

01 

049 

7 

23 

38 

105 

94 

850 

59 

594 

94 

337  99799 

078 

7 

22 

39 

134 

94 

879 

59 

623 

93 

366   97 

107 

7 

21 

40 

164 

93 

908 

58 

653 

92 

395 

95 

136 

6 

20 

41 

193 

93 

938 

57 

682 

90 

424 

93 

165 

6 

19 

42 

222 

93 

967 

56 

711 

89 

453 

92 

194 

04 

IS 

43 

251 

92 

996 

55 

740 

8 

482 

90 

223 

6 

17 

44 

280 

92 

030251   54 

769 

8 

511 

88 

252J 

16 

45 

309J   91 

054   53 

798 

8 

540 

86 

281 

15 

46 

01338:99991 

0308399952 

"0482799883 

06569 

99784 

08310996 

~ 

47 

367i   91 

112i   52 

856!   8 

598 

82 

339; 

] 

48 

396!   90 

14l|   51 

885   8 

627 

80 

368 

j 

49 

425 

90 

170|   50 

914 

7 

656 

78 

397 

] 

50 

454   89 

199   49 

943 

685 

76 

426 

51 

483   89 

228 

48 

972 

114 

7' 

455; 

52 

513   89 

257 

47 

05001 

7 

743 

7s 

484! 

53 

5425   88 

286 

46 

030 

7 

773 

70 

513 

54 

571!   88 

316 

45 

059J   7 

802 

6S 

542 

55 

600   8 

345 

44 

OS8|   7 

831 

66 

571 

56 

629   8 

374 

43 

117!   6S 

86C 

64 

600 

5' 

658   8 

40? 

42 

146   6 

88& 

62 

629 

5£ 

6871   8 

432 

4 

175   6 

91S 

6C 

65S   i. 

5J 

7161   8 

461 

4C 

205!   & 

94' 

5 

687;   2 

y 

N7CX  Nat 

N.C- 

^NaT 

N.C-  Nat 

N.C- 

Nat 

N.C^ 

•  Na 

Sine  Sine 

Sine 

Sine 

Sine  Sin 

Sine  Sine 

Sine 

Sin 

89  Deg. 

88  Deg. 

87  Deg 

86  Deg 

85  Deg 

130 


A  TABLE  OF  NATURAL  SINES. 


5  Deg. 

6  Deg. 

7  Deg. 

8  Deg. 

9T>eg. 

M 

N.  S.  N.CS  N.  S.N.Cri.|N.  S.jN.CS 

N.  S.  N.Cfc*. 

N.  g^iN.CS 

M 

~0 

08716  99619  10453  98452"  12187  99255 

13917  99027 

1564398769 

"60 

1 

745   17 

482 

49 

216 

51 

946;   23 

672 

64 

59 

2 

774   14 

511 

46 

245 

43 

975|   19 

701 

60 

58 

3 

803   12 

540 

43 

274 

44 

14004   15 

730 

55 

67 

4 

831 

09 

569 

40 

302 

40 

033   11 

758 

61 

56 

5 

860!   07 

697 

37 

331 

37 

061 

06 

787 

46 

55 

6 

889   04 

626 

34 

360 

33 

090   02 

816 

41 

64 

7 

918!   02 

655 

31 

389 

30 

11998998 

845 

37 

53 

8 

947  99599 

684 

28 

418 

26 

148   94 

873 

32 

5? 

9 

976;   96 

713 

24 

447 

22 

177   10 

902 

28 

51 

1009005!   94 

742 

21 

476 

19 

205   86 

931 

23 

60 

11  034   91 

771   18 

504 

15 

234i   82 

959 

18 

49 

12J  063   88 

800   15 

533 

11 

263   78 

988 

14 

48 

1S|  092   86 

829 

12 

562 

08 

292   73 

16017 

09 

47 

14  121   83 

858   69 

591 

04 

320   69 

046 

04 

46 

15  150   80 

887   06 

620 

00 

349   65 

074   00 

45 

1609179  99578] 

10916  99402 

1-2649 

99197 

14378  98961 

1610398(695 

~44 

17 

208   75 

94599399 

678 

93 

407   57 

132 

90 

43 

18 

237   72 

973 

96 

706 

89 

436   53 

160 

86 

42 

19 

266!   70 

11002 

93 

735 

86 

464   48 

189 

81 

41 

20 

295|   67 

031 

90 

764 

82 

493 

44 

218 

76 

40 

21 

324!   64 

060 

86 

793 

78 

622 

40 

246 

71 

39 

22 

353   62 

089 

83 

822 

75 

561 

36 

275 

67 

38 

23 

382 

59 

118 

80 

851 

71 

580 

31 

304 

62 

37 

24 

411!   56 

147 

77 

880 

67 

608 

27 

333 

57 

36 

25 

440   53 

176 

74 

908 

03 

637 

23 

361 

52 

35 

26 

469   51 

205 

70 

937 

60 

666 

19 

390 

48 

34 

27 

498   48 

234 

67 

966 

56 

695 

14 

419 

43 

33 

28!  5271   45 

263   64 

995 

62 

723 

10 

447 

38 

32 

29 

556)   42 

291   60 

13024 

48 

752 

06 

476 

33 

31 

30 

5851   40 

320 

57 

063 

44 

781 

02 

505 

29 

30 

31  09614  99537 

11  349  '99354 

3081 

99141 

14810 

98897 

16533 

98624 

29 

32  642i   34 

378 

51 

110 

37 

838 

93 

662 

19 

28 

33  671   31 

407 

47 

139 

33 

867 

89 

591 

14 

27 

34'  700   28 

436 

44 

168 

29 

896 

64 

620 

09 

26 

35 

729 

26 

465 

41 

197 

25 

925 

80 

648 

04 

25 

36 

758   23 

494 

37 

226 

2-2 

954 

76 

677 

00 

24 

37>  787   20 

523)   34 

254 

18 

982 

71 

706 

98595 

23 

38 

616   17 

652 

31 

283 

14 

15011 

67 

734 

90 

22 

39 

845 

14 

680 

27 

312 

10 

040 

63 

763 

8j 

21 

40 

874 

11 

609 

24 

341 

06 

069 

58 

792 

80 

20 

41 

903 

08 

638 

20 

370 

02 

097 

54 

820 

75 

19 

42 

932 

06 

667 

17 

399  99098 

126 

49 

849 

70 

18 

43 

961 

03 

696 

14 

427;   94 

155 

45 

878 

65 

17 

44 

990 

00 

725 

10 

456   91 

184 

41 

906 

61 

16 

45 

10019  99497 

754   07 

485!   87 

212 

36 

935 

56 

15 

46 

10048  99494  11783  99303 

13514  99083 

15241 

98832 

16964 

98551 

14 

47 

077 

91  812'   W 

543   79 

270 

27 

992 

46 

13 

48 

106 

88 

840  99297 

572   75 

292 

23 

17021 

41 

12 

49 

135 

85 

869 

93 

6001   71 

327 

18 

050 

36 

11 

50 

164 

82 

698 

90 

629!   67 

356 

I/ 

078 

31 

10 

51 

192 

79 

927 

86 

658   63 

386 

09 

107 

26 

9 

52 

221 

76 

956 

83 

687 

59 

414 

05 

136 

21 

8 

53 

250 

73 

985 

79 

716 

55 

442 

00 

164 

16 

*t 

54 

279 

70 

12014 

76 

744J   51 

471 

98796 

193 

11 

6 

55 

308 

67 

043 

72 

773   47«  500 

91 

222 

06 

i 

56 

337 

64 

071 

69 

802   43:  529 

87 

250 

01 

4 

57 

366 

61 

100 

65 

831   39'  557 

82 

279 

98496 

e 

58 

395 

68 

129 

62 

8601   35'  586 

78 

308 

91 

2 

59 

424 

65 

158 

68 

889|  .31  615 

73 

336 

86 

1 

~M 

N.CS 

NTS: 

N.CS 

N.  8. 

N.CS.N.  S.;N.CS 

N.  S. 

N.CS. 

N.  S. 

M 

84  Deg. 

83  Deg. 

82  Deg.  81  Deg. 

80  Deg. 

A  TABLE  OF  NATURAL  SINES. 


131 


10  beg.  11  Deg. 

2  Deg.,13  Deg. 

14  Deg. 

M 

N.  S. 

\.CS  N.  S. 

N.CS 

iv.  s.  N.CS'N.  s.  N.CS 

N.  S.  N.CS 

M 

0 

17366 

98481  19081  98163 

Z0791  97815'22495  97437 

24192  97030 

"60 

1 

393 

76  109! 

57 

820  809  523  430 

220  023 

59 

2 

422 

71   138 

52 

848;  803!  552 

424 

249  015 

58 

3 

451 

66r  167 

46 

877  i  797 

580 

417 

277  008 

57 

4 

479 

61   195 

40 

905  791 

608 

411 

305  001 

66 

5 

508 

55;  224 

35 

933,  784  637 

404 

333  96994 

56 

6 

537 

50  252 

29 

962  77$  665 

398 

362  987 

54 

7 

565 

45  281 

24 

990  772f  693!  391 

390  980 

53 

8 

594 

40  309 

18 

21019  7665  722!  384 

418  973 

52 

9 

623 

35-  338 

12 

047  7601  750!  378 

446  966 

51 

10 

651 

30  366 

07 

076  7641  778 

371 

474  969 

50 

11 

680 

25\  395 

01 

104  748-  807 

365 

503  962 

49 

12 

708 

20  42398096 

132  7425  835 

358 

531  945 

48 

13 

737 

14  452 

90 

161  735i  863 

351 

559  937 

47 

14 

766 

09'  481 

84 

189  729J  892 

345 

587  930 

46 

15 

794 

04-  5U9 

79 

218  723*  920 

338 

615  923 

45 

16 

1782tf 

983991953898073 

212415  97717122948 

97331 

24644  96916 

44 

17 

852 

94;  566 

67 

275  711?  977 

325 

672  909 

43 

18 

680 

89  >  69  j 

61 

303 

705;23005 

318 

700 

902 

42 

19 

909 

83'  623 

56 

331 

698;  033 

311 

728 

894 

41 

20 

937 

78i  652|   50 

360 

692?  062 

304 

756  887 

40 

21 

966 

73  680i   44 

388 

686$  090 

298 

784  880 

39 

22 

995 

68 

709 

39 

417 

680'  118 

291 

813  873 

38 

'23 

18023 

62 

737 

33 

445 

673;  146 

284 

841  866 

37 

24 

052 

57 

766|   27 

474 

667J  175 

278 

869  858 

36 

25 

081 

52 

794i   21 

502 

661  203 

271 

897  851 

35 

26   109 

47, 

8231   16 

530 

655°  231 

264 

925  844 

34 

27   138 

41 

851 

10 

659 

648?  260 

257 

953  837 

33 

28 

166 

36 

880 

04 

587 

642?  288 

251 

982  829 

32 

29 

195 

31 

90s  97998 

616 

6J6-  316 

24425010  822 

31 

30  224 

25;  937 

92 

644 

630!  345 

237 

038  315 

30 

SM8252 

9832019965979*7 

21672 

97623  23373 

97230  25066  96807 

29 

32  281 

15:  994 

81 

701 

617-'  401 

223 

094;  800 

28 

S3  309 

10'2(X>22 

75 

729 

61  1  429 

217 

122  793 

27 

34!  338 

04  061 

69 

75,-i 

604-  458 

210 

151  786 

26 

35  367 

98299^  079J   63 

786 

598 

486 

203 

179  778 

25 

36!  395 

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58 

814 

592 

514 

196 

207 

771 

24 

37   424 

88;  136 

62 

843 

586 

542 

189 

235 

764 

23 

38  452 

831  165 

46 

871 

579 

571 

182 

263 

756 

22 

39  481 

77   193 

40 

899 

573 

599 

176 

291 

749 

21 

40  509 

72 

222 

34 

928 

566 

627 

169 

320|  742 

20 

41 

538 

67 

250 

28 

956 

660 

656 

162 

348!  734 

19 

42 

567 

61 

279 

22 

985 

553 

684 

155 

376 

727 

18 

43 

595 

56 

307 

16 

22013 

547 

712 

148 

404 

719 

17 

44 

624 

50 

336 

10 

041   641 

740 

141 

432 

712 

16 

45 

652 

45 

364 

05 

0/0!  534 

769 

134 

460 

705 

15 

~4G 

18681  98240  2^93 

97899 

2209897528 

23797  97127^25488 

96697 

14 

47 

710 

34'  421 

93 

126  621 

826 

120 

516 

690 

13 

48 

738 

29 

450i   87 

155  615 

853 

113 

545 

682 

12 

49 

767 

23 

478J   81 

183|  508 

882 

106 

573 

67o 

11 

50 

795 

18 

507 

7o 

212  502 

910 

100 

601 

667 

10 

51 

824 

12 

535 

69 

240 

496 

936 

093 

629 

660 

c 

52 

852 

07 

563 

63 

268 

489 

966 

086 

657 

653 

| 

53 

881 

01 

592 

57 

297  483 

995 

079 

685 

645 

54 

910  98196 

620 

51 

325 

476  24023 

072 

713 

638 

6 

55 

938   90 

649 

45;  353 

470 

051 

065 

741 

630  5 

56 

967 

85 

677 

39-  382 

463 

079 

058 

769 

623  4 

57 

995 

79 

706 

33  410 

457 

108 

061 

798 

615  S 

58 

19024 

74 

734 

27  438 

450 

136 

044 

826 

608 

2 

59 

052 

68 

763   21}  467 

444 

164 

037 

854 

eoo;  i 

~M 

N.CS 

N.  S. 

N.CS 

N.  S.rN.CS  JN.  S. 

N.CS  N.  S. 

N.CS 

N.  S. 

M 

79  Deg. 

78  Deg.  77  Deg.<76  Deg.  75  Deg. 

A  TABLE  OF  NATURAL  SINES. 


15  Deg. 

16  Deg. 

17  Deg. 

18  Deg. 

19  Deg. 

M 

N.  S. 

N.CS 

N.  8. 

N.CS 

N.  S. 

N.CS 

N.  S.iN.CS 

N.  S. 

N.CS 

M 

~0 

25882 

96593 

27564 

96126 

29237 

95630 

3090295106 

32557 

94552 

60 

1 

910 

585 

592 

118 

265 

622 

929 

097 

584 

542 

59 

2 

938 

678 

620 

110 

293 

613 

957 

088 

612 

533 

58 

3 

966 

570 

648 

102 

321 

606 

985 

079 

639 

523 

57 

4 

994 

562 

676 

094 

348 

596 

31012 

070 

667 

514 

56 

5 

26022 

555 

704 

086 

376 

588 

040 

061 

694 

504 

55 

6 

050 

547 

731 

078 

404 

679 

068 

062 

722 

495 

54 

7 

079 

540 

759 

070 

432 

571 

095 

043 

749 

485 

53 

8 

107 

532 

787 

062 

460 

562 

123 

033 

777 

476 

62 

9 

135 

624 

815 

054 

487 

554 

151 

024 

804 

466 

51 

10 

163 

517 

843 

046 

515 

545 

178 

015 

832 

457 

50 

11 

191 

509 

871 

037 

543 

536 

206 

006 

859 

447 

49 

12  219 

502 

899 

029 

571 

528 

233 

94997 

887 

438 

48 

13)  247 

494 

927 

021 

599 

519 

261 

988 

914 

428 

47 

141  275 

486 

955 

013 

626 

511 

289 

97-9 

942 

418 

46 

15;  303 

479 

983 

005 

654 

502 

316 

970 

969 

409 

45 

162633196471 

28011  '95997 

29682 

95493 

31344 

94961 

32997 

94399 

"44 

17!  359 

463 

039  989 

710 

485 

372 

952 

33024 

390 

43 

18  387 

456 

067  981 

737 

476 

399 

943 

051 

380 

42 

19  415 

448 

095!  972 

765 

467 

427 

933 

079 

370 

41 

20  443 

440 

123  964 

793 

459 

454 

924 

106 

361 

40 

2l!  471|  433 

150 

956 

821 

450 

482 

915 

134 

35] 

39 

22  500  425 

178 

948 

849 

441 

510 

906 

161 

342 

38 

23  528  417 

206 

940 

876 

433 

537 

897 

189 

332 

37 

24  556  410 

234 

931 

904 

424 

565 

888 

216 

322 

36 

25  584  402 

262 

923 

932 

415 

593 

878 

244 

313 

35 

26  612  394 

290 

915 

960 

407 

620 

869 

271 

303 

34 

27  640  386 

318 

907 

987 

398 

648 

860 

298 

893 

33 

28  668 

379 

346 

898 

30015 

389 

675  851 

326 

284 

32 

29;  696 

371 

374!  890 

043 

380 

703  842 

353 

274 

31 

30'  724 

363 

402 

882 

071 

372 

730)  832 

381 

264 

SO 

312675296355 

28429 

95874 

30098195363 

31758 

94823 

33408 

94254 

29 

32|  780J  347 

457 

865 

126 

354 

786 

814 

436 

245 

28 

33  808!  340 

485 

857 

154 

345 

813 

805 

463 

235 

27 

34  836 

332 

513 

849 

182 

337 

841 

795 

490 

225 

26 

35  864 

324 

541 

841 

209 

328 

868 

786 

518 

215 

25 

36  892 

316 

569 

832 

237 

319 

896 

777 

545 

206 

24 

37  920 

308 

597 

824 

265 

310 

923 

768 

573 

196 

23 

38  948 

301 

625 

816 

292 

301 

951 

758 

600 

186 

22 

39  976 

293 

652 

807 

320 

293 

978 

749 

627 

176 

21 

4027004 

286 

680 

799 

348 

284 

32006 

740 

655 

167 

20 

41 

032 

277 

708 

791 

376 

275 

034 

730 

682 

157 

19 

42 

060 

269 

736 

782 

403 

266 

061 

721 

710 

147 

18 

43 

088 

261 

764 

774 

431 

257 

089 

712 

737 

137 

17 

44 

116 

263 

792 

766 

459 

248 

116 

702 

764 

127 

16 

45 

__144 

246 

820 

757 

486 

240 

144 

693 

792 

118 

15 

46 

27172 

96238 

28847 

95749 

30514195231 

32171 

94684 

33819 

94108 

14 

47 

200 

230 

875 

740 

542  222 

199 

674 

846 

098 

13 

48 

228 

222 

903 

732 

570  213 

227 

665 

874 

088 

12 

49 

256 

214 

931 

724 

697 

204 

254 

656 

901 

078 

11 

50 

284 

206 

959 

715 

625 

195 

282 

646 

929 

068 

10 

51 

312 

198 

987 

707 

653 

186 

309 

637 

956 

058 

9 

52 

340 

190 

29015 

698 

680 

177 

337 

627 

983 

049 

8 

53 

368 

182 

042 

690 

708 

168 

364 

618 

34011 

039 

7 

54 

396 

174 

070 

681 

736 

159 

392 

609 

038 

029 

6 

55 

424 

166 

098 

673 

763 

150 

419 

699 

065 

019 

5 

56 

452 

158 

126 

664 

791 

142 

447 

590 

093 

009 

4 

57 

480 

150 

154 

656 

819 

133 

474 

580 

120 

93999 

3 

58 

508 

J42 

182 

647 

846 

124 

502 

571 

147 

989 

2 

59 

636 

134 

209 

639 

874 

115 

529 

561 

175 

979 

Jd 

N.CS 

N.  S. 

N.CS 

N.S. 

N.CS 

N.  S. 

N.CS 

N.  ,S. 

N.CS 

N.  S. 

M 

74  Deg. 

73  Deg.J72  Deg. 

71  Deg.l 

70  Deg.!  1 

A  TABLE  OP  NATURAL  SINES. 


13S 


20  Deg.  21  Deg. 

2T)eg.  23  Seg.24  Deg. 

M 

\r.  S.  N.CS  N.  8.  N.Tc 

.  S.  N.CS  N.  S.N.CS'JS.  S.  N.CS 

M 

C 

34202939693583793158 

7461  92718  39073  92050  40674  91355 

60 

1 

229  959  864  348 

488  707   100  039  700  343 

59 

2 

257  949  891  337 

515,  697  127  028  727  331 

58 

3 

284  939  918'  327 

542:  686  153  016  753  310 

51 

4 

311  929  945  3it> 

569  1  675  180  005  780  307 

56 

5 

339  919  973  306 

595!  664  20791994  806  295 

55 

6 

366  909  36000  295 

622!  653  234  982:  833  283 

& 

7 

393  899  027  285 

649!  642  260  971  860  272 

5t 

8 

421  889  054  274 

676  631  287  959  886  260 

55 

9 

448  879  081  264 

703i  620  314  948  913  248 

51 

10 

475  869   108  253 

730;  609  341  936  939  236 

50 

11 

603  859   135  243 

757  1  598  367  925  966  224 

49 

12 

530  849   162  232 

784'  587  394  914  992  212 

48 

13 

557  839   190  222 

811!  576.  421  90241019  200 

47 

14 

584  829  217  211 

838  565  448  891  045  188 

46 

15 

612   819  244  201 

865  554  474  879  072  176 

45 

16 

34639  93809  36271  93190 

7892  92543  39501  91868  41098  §1164 

~4 

17 

666 

799   298   180 

919;  632  528  856  125  162 

45 

18 

694 

739  325  169 

946;  621  555  845  151   140 

42 

19 

721 

779  352  159 

9731  510  581  833  178  128 

41 

20 

748 

769  379  146 

999  1.  499  608  822:  204  116 

40 

21 

775 

759  406  137 

8026  488  635  810  231   104 

39 

22 

803 

748  434  127 

053  477  661  799  257  092 

38 

2° 

830 

738  461   116 

0801  466  6881  787  284  080 

37 

24 

857 

728  488  106 

107J  465  715  775  310  O6 

36 

!5 

884 

718  515  096 

134;  444  741   764;  337  05 

35 

2b 

912 

708  542  084 

161J  432  768  752]  363  044 

34 

27 

939 

698  669  074 

188|  421  795  741}  390  03 

33 

28 

966 

688  596  063 

215}  410  822!  729J  416  02 

32 

2J 

993 

677  623  052 

241:  399  848  718<  443  00 

3 

30 

35021. 

667  650  042 

268  388  875  70$  4699099 

3 

In 

35048 

3857  36677  93031 

38295  92377  39902  91694'41496  90984 

29 

32 

075 

647  704  0^0 

322  366  928  683!  522  97 

28 

33 

102 

637  '<31  010 

349;  355  955  67l]  549  96 

27 

34 

130 

626-  758^2999 

376|  343  982i  660]  575  94 

26 

35 

157 

616  785  988 

403  332:40008  648  602  93 

C 

36 

183 

606  812  978 

430  321  035  636  628  924 

C 

37 

211 

596  839|  967 

456  310]  062  625J  655  91 

C 

38 

239 

585  867i  956 

483  299j  088  613  681  89 

C 

39 

266 

575  894  94 

510  287]  115  601i  707  88 

C 

40!  293 

665  921  93 

537  276*  141  590]  734  87 

C 

41  320 

555  948  92 

564  2651  198  578   760  86 

42  347 

544  975  91 

59  li  264  195  568  787  85 

• 

43i  375 

534  37002  90 

617.  243   221   5551  813   83 

44 

402 

524  029   89 

644  231   248!  543J  840  82 

429 

514  056   88 

671  220  276  53L  866;  81 

46,35456 

47j  484 

93503  37083  9287 
493  110  85 

33698  92209|4030ll91519gl892  90803 
725  1981  328  6081  919  79( 

48|  511 

483  137  84 

752  186?  355|  496]  945  7" 

49  538 

472   164  83 

778  175;  381  484!  972  76 

5( 

)  565 

462,  191  82 

805  164|  408  472'  998  75 

5 

I  592 

452  218  81 

832  152?  434  461420241  74 

52  619 

441?  245  80 

859,  14i;  461  449  051!  72 

53,  647 

43l|  272  79 

836  130  488  437-'  077!  71 

54  674 

4201  299  78 

912!  119?  514  426J  104  70 

55  70 

a  326  773  939!  107^  641J  414J  130  692  6 

56  72 

353  762  966!  096  567  402?  156>  680  i 

57,  75 

380  751  9931  085  594  390]  183  668!  3 

68  78 

379*  407  74039020  073  621  378]  209  655:  g 

69  81 

388  434  729  046|  062  647  366'  235  643   1 

J69  Deg.;68  Deg.;67  Deg.^66  Deg.65  Deg. 

134 


A  TABLE  OF  NATURAL  SINES. 


•I 

1 

25  Deg.pG 

beg 

27 

Deg.)28 

Deg 

29  Deg 

M 

[N.  8 

N.«  •  iV.  S.  N.i.-S 

x.  >. 

\..VSJN.  S.  N.CS 

.V.  S. 

N.CS 

042262 

90631*4383789879 

45399  891014694 

7  8829o 

48481 

87462,  '60 

1 

28S 

618S  86 

3  867 

42 

5  087 

97 

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I 

A  TABLE  OF  NATURAL  SINES. 


135 


30  Deg.  31  Deg.  32  Deg. 

33  Deg.  34  Deg. 

M 

N.  S.jN.CS  N  H  N.CS  N  S.iN.CB 

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0 

50000186603  61504 

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54464  83867  55919  82904  60 

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588  529 

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488  851  943  887,  58 

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573  654 

687  041  i  774 

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559  579 

672  066'  759 

537  819  992'  855  57 

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101 

544  604 

657  091!  743 

561  80456016  839  56 

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126 

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151 

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252 

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55ll  263  635 

732  692.  184  724  49 

12 

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536,  288  619 

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136 


A  TABLE  OF  NATURAL  SINES, 


35  Deg.  (36  DegJ 

37  Deg. 

38  Deg.'39  Deg. 

M 

0 

N.  S.  .N.CS  IN.  S.'N.CS.'N.  S.  N.CS.  N.  S.  N.CS 
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205  846 

589 

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7651  990J  748 

390  706 

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414  688 

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158  631 

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437  671 

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180  513 

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460  653 

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14 

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681   108 

662f  506  b!8>  887 

550 

248  458 

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15 

715  664J  131 

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5321 

271  439 

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16 
17 

57738  81647S9154  80627)60553  79583  61932  7851463293  7742li  44 
7621  631   178  610|  576  565  955  496J  316  402  43 

18 

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614  201'  59SC  599  547 

978 

478 

338  384 

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361:  366  41 

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383  347 

40 

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563  272 

541 

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22 

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546-  295 

524 

6b'l   477]  069 

405 

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530  318 

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387 

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24 

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513  342 

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473!  273 

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496  365 

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761  424*  138 

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333 

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34 

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428  459 

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5861  181 

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412  482 

386J  876  335 

251  261 

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31  58094  81395  59506  8u368'608»9  79318  62274  7824463630  77144J  29 

32  118 

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351 

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334*  945'  282;  320|  206 

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34  165 

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316|  968,  264  342 

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327  599 

299*  991;  247J  365 

170 

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36  212 

310  622 

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199  087 

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NXJiTN.  Si 

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N.CS. 

N.  S. 

M 

54 

Deg.>53 

Deg. 

52  Deg. 

61  Deg. 

50  Deg, 

i 

A  TABLE  OP  NATURAL  SINES. 


42  PegT43  Peg.]  44  Peg 

f.  S.   .  CSIN.  S.  N.  CSfN.  S.iN.Ci 


4314.68200  73135  69466  71934 


4002  68539  72817  69800  71610 


88&  666  697  925  488 


865  688  677  946  468 


846   709   657   966  447 


826  730  637  987  427 


751  61770008  407 


787,*  772,  597  029  386 


793:  577  049 

814  557-  070  345 

835  537  091  325 


3708  68857  7251?  701 12  71305 


73412  69172  72216  70422  70998 


604-  76 

585'  78 

566  80 

547'  82 


451  05 

431  07 

412.  OS 

392,  11 


49  DegJ  48  Peg.  47   Peg.  46   Peg.  45  DegJ_ 


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